Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of model order reduction techniques in various engineering and scientific applications including but not limited to mechanical, naval and aeronautical engineering. The focus here is kept limited to computational fluid mechanics and related applications. The advances in the reduced order modeling with proper orthogonal decomposition and reduced basis method are presented as well as a brief discussion of dynamic mode decomposition and also some present advances in the parameter space reduction. Here, an overview of the challenges faced and possible solutions are presented with examples from various problems.

1 aRozza, Gianluigi1 aMalik, M.H.1 aDemo, Nicola1 aTezzele, Marco1 aGirfoglio, Michele1 aStabile, Giovanni1 aMola, Andrea uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85075395686&partnerID=40&md5=fb0b1a3cfdfd35a104db9921bc9be67500478nas a2200133 4500008004100000245006600041210006600107260001600173300001200189490000700201100002300208700001600231856009700247 2019 eng d00aActivation of a muscle as a mapping of stress–strain curves0 aActivation of a muscle as a mapping of stress–strain curves bElsevier BV a37–420 v281 aRiccobelli, Davide1 aAmbrosi, D. uhttps://www.math.sissa.it/publication/activation-muscle-mapping-stress%E2%80%93strain-curves00414nas a2200109 4500008004100000245010800041210006900149300001100218100002100229700001700250856003700267 2018 eng d00aAccelerating the iterative solution of convection-diffusion problems using singular value decomposition0 aAccelerating the iterative solution of convectiondiffusion probl a1–211 aPitton, Giuseppe1 aHeltai, Luca uhttps://arxiv.org/abs/1807.0946700480nas a2200145 4500008004100000022001400041245007600055210006900131300001600200490000700216100002100223700002900244700002300273856003800296 2018 eng d a0025-571800aAdaptive discontinuous Galerkin methods for elliptic interface problems0 aAdaptive discontinuous Galerkin methods for elliptic interface p a2675–27070 v871 aCangiani, Andrea1 aGeorgoulis, Emmanuil, H.1 aSabawi, Younis, A. uhttps://doi.org/10.1090/mcom/332201047nas a2200133 4500008004100000245007000041210006900111300001400180490000700194520062800201100002400829700002100853856003900874 2018 eng d00aAnalysis of a Dynamic Peeling Test with Speed-Dependent Toughness0 aAnalysis of a Dynamic Peeling Test with SpeedDependent Toughness a1206-12270 v783 aWe analyse a one-dimensional model of dynamic debonding for a thin film, where the local toughness of the glue between the film and the substrate also depends on the debonding speed. The wave equation on the debonded region is strongly coupled with Griffith's criterion for the evolution of the debonding front. We provide an existence and uniqueness result and find explicitly the solution in some concrete examples. We study the limit of solutions as inertia tends to zero, observing phases of unstable propagation, as well as time discontinuities, even though the toughness diverges at a limiting debonding speed.

1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttps://doi.org/10.1137/17M114735400579nas a2200145 4500008004100000245010500041210006900146300001600215490000700231100001500238700001600253700001700269700001800286856012900304 2018 eng d00aAn authenticated theoretical modeling of electrified fluid jet in core–shell nanofibers production0 aauthenticated theoretical modeling of electrified fluid jet in c a1791–18110 v471 aRafiei, S.1 aNoroozi, B.1 aHeltai, Luca1 aHaghi, A., K. uhttps://www.math.sissa.it/publication/authenticated-theoretical-modeling-electrified-fluid-jet-core%E2%80%93shell-nanofibers01821nas a2200181 4500008004100000024003700041245012000078210006900198520118600267653002301453653002601476100002201502700001901524700002101543700001701564700002101581856003701602 2017 eng d ahttps://arxiv.org/abs/1701.0342400aAdvances in Reduced order modelling for CFD: vortex shedding around a circular cylinder using a POD-Galerkin method0 aAdvances in Reduced order modelling for CFD vortex shedding arou3 aVortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. In this work a Reduced Order Model (ROM) of the incompressible flow around a circular cylinder, built performing a Galerkin projection of the governing equations onto a lower dimensional space is presented. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pressure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) for this purpose the projection of the Governing equations (momentum equation and Poisson equation for pressure) is performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework are presented. The accuracy of the reduced order model is assessed against full order results.

10afinite volume, CFD10aReduced order methods1 aStabile, Giovanni1 aHijazi, Saddam1 aLorenzi, Stefano1 aMola, Andrea1 aRozza, Gianluigi uhttps://arxiv.org/abs/1701.0342402169nas a2200109 4500008004100000245012900041210006900170520172600239100002401965700002201989856004802011 2017 en d00aAlmost global existence of solutions for capillarity-gravity water waves equations with periodic spatial boundary conditions0 aAlmost global existence of solutions for capillaritygravity wate3 aThe goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size ϵ, is almost globally defined in time on Sobolev spaces, i.e. it exists on a time interval of length of magnitude ϵ−N for any N, as soon as the initial data are smooth enough, and the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, our method is based on a normal forms procedure, in order to eliminate those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations are a quasi-linear system, usual normal forms approaches would face the well known problem of losses of derivatives in the unbounded transformations. In this monograph, to overcome such a difficulty, after a paralinearization of the capillarity-gravity water waves equations, necessary to obtain energy estimates, and thus local existence of the solutions, we first perform several paradifferential reductions of the equations to obtain a diagonal system with constant coefficients symbols, up to smoothing remainders. Then we may start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization.The reversible structure of the water waves equations, and the fact that we look for solutions even in x, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.1 aBerti, Massimiliano1 aDelort, Jean-Marc uhttp://preprints.sissa.it/handle/1963/3528501295nas a2200133 4500008004100000245006800041210006800109300001200177490000700189520087800196100002001074700002101094856004601115 2017 eng d00aAnalytic geometry of semisimple coalescent Frobenius structures0 aAnalytic geometry of semisimple coalescent Frobenius structures a17400040 v063 aWe present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.

1 aCotti, Giordano1 aGuzzetti, Davide uhttps://doi.org/10.1142/S201032631740004400564nas a2200133 4500008004100000245012900041210006900170260008500239300001400324490000700338100002300345700001900368856004300387 2017 eng d00aAn application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators0 aapplication of coincidence degree theory to cyclic feedback type bNicolaus Copernicus University, Juliusz P. Schauder Centre for Nonlinear Studies a683–7260 v501 aFeltrin, Guglielmo1 aZanolin, Fabio uhttps://doi.org/10.12775/TMNA.2017.03801212nas a2200109 4500008004100000245010500041210006900146520071800215100002100933700002100954856012700975 2017 eng d00aOn the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics0 aApplication of Reduced Basis Methods to Bifurcation Problems in 3 aIn this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

1 aPitton, Giuseppe1 aRozza, Gianluigi uhttps://www.math.sissa.it/publication/application-reduced-basis-methods-bifurcation-problems-incompressible-fluid-dynamics00875nas a2200193 4500008004100000022001400041245006900055210006600124300001600190490000800206520024700214653002900461653002400490653002300514653003300537100002200570700001800592856007100610 2017 eng d a0022-039600aAn avoiding cones condition for the Poincaré–Birkhoff Theorem0 aavoiding cones condition for the Poincaré–Birkhoff Theorem a1064 - 10840 v2623 aWe provide a geometric assumption which unifies and generalizes the conditions proposed in [11], [12], so to obtain a higher dimensional version of the Poincaré–Birkhoff fixed point Theorem for Poincaré maps of Hamiltonian systems.

10aAvoiding cones condition10aHamiltonian systems10aPeriodic solutions10aPoincaré–Birkhoff theorem1 aFonda, Alessandro1 aGidoni, Paolo uhttp://www.sciencedirect.com/science/article/pii/S002203961630327800504nas a2200157 4500008004100000022001400041245007000055210006900125300001800194490000700212100002100219700002900240700001600269700002200285856003900307 2016 eng d a1064-827500aAdaptivity and blow-up detection for nonlinear evolution problems0 aAdaptivity and blowup detection for nonlinear evolution problems aA3833–A38560 v381 aCangiani, Andrea1 aGeorgoulis, Emmanuil, H.1 aKyza, Irene1 aMetcalfe, Stephen uhttps://doi.org/10.1137/16M106073X02112nas a2200217 4500008004100000245018600041210006900227260003600296520123100332100002501563700002401588700002001612700001701632700001901649700002101668700002101689700002101710700001701731700001601748856013001764 2016 en d00aAdvances in geometrical parametrization and reduced order models and methods for computational fluid dynamics problems in applied sciences and engineering: overview and perspectives0 aAdvances in geometrical parametrization and reduced order models aCrete, GreecebECCOMASc06/20163 aSeveral problems in applied sciences and engineering require reduction techniques in order to allow computational tools to be employed in the daily practice, especially in iterative procedures such as optimization or sensitivity analysis. Reduced order methods need to face increasingly complex problems in computational mechanics, especially into a multiphysics setting. Several issues should be faced: stability of the approximation, efficient treatment of nonlinearities, uniqueness or possible bifurcations of the state solutions, proper coupling between fields, as well as offline-online computing, computational savings and certification of errors as measure of accuracy. Moreover, efficient geometrical parametrization techniques should be devised to efficiently face shape optimization problems, as well as shape reconstruction and shape assimilation problems. A related aspect deals with the management of parametrized interfaces in multiphysics problems, such as fluid-structure interaction problems, and also a domain decomposition based approach for complex parametrized networks. We present some illustrative industrial and biomedical problems as examples of recent advances on methodological developments.

1 aSalmoiraghi, Filippo1 aBallarin, Francesco1 aCorsi, Giovanni1 aMola, Andrea1 aTezzele, Marco1 aRozza, Gianluigi1 aPapadrakakis, M.1 aPapadopoulos, V.1 aStefanou, G.1 aPlevris, V. uhttps://www.math.sissa.it/publication/advances-geometrical-parametrization-and-reduced-order-models-and-methods-computational01524nas a2200157 4500008004100000245011100041210006900152300001000221490000700231520095900238653002001197100002501217700001801242700002201260856008401282 2016 en d00aOn the area of the graph of a piecewise smooth map from the plane to the plane with a curve discontinuity0 aarea of the graph of a piecewise smooth map from the plane to th a29-630 v223 aIn this paper we provide an estimate from above for the value of the relaxed area functional for a map defined on a bounded domain of the plane with values in the plane and discontinuous on a regular simple curve with two endpoints. We show that, under suitable assumptions, the relaxed area does not exceed the area of the regular part of the map, with the addition of a singular term measuring the area of a disk type solution of the Plateau's problem spanning the two traces of the map on the jump. The result is valid also when the area minimizing surface has self intersections. A key element in our argument is to show the existence of what we call a semicartesian parametrization of this surface, namely a conformal parametrization defined on a suitable parameter space, which is the identity in the first component. To prove our result, various tools of parametric minimal surface theory are used, as well as some result from Morse theory.

10aArea functional1 aBellettini, Giovanni1 aTealdi, Lucia1 aPaolini, Maurizio uhttps://www.esaim-cocv.org/articles/cocv/abs/2016/01/cocv140065/cocv140065.html00479nas a2200133 4500008004100000022001400041245010000055210006900155300002800224490000700252100001900259700002200278856004500300 2016 eng d a1815-065900aOn asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight0 aasymptotic regimes of orthogonal polynomials with complex varyin aPaper No. 118, 50 pages0 v121 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.3842/SIGMA.2016.11801380nas a2200133 4500008004300000245007200043210006900115260001500184520093400199100001901133700001801152700002501170856005101195 2015 en_Ud 00aAnisotropic mean curvature on facets and relations with capillarity0 aAnisotropic mean curvature on facets and relations with capillar bde Gruyter3 aWe discuss the relations between the anisotropic calibrability of a facet F of a solid crystal E, and the capillary problem on a capillary tube with base F. When F is parallel to a facet of the Wulff shape, calibrability is equivalent to show the existence of an anisotropic subunitary vector field in $F, with suitable normal trace on the boundary of the facet, and with constant divergence equal to the anisotropic mean curvature of F. When the Wulff shape is a cylynder, assuming E convex at F, and F (strictly) calibrable, such a vector field is obtained by solving the capillary problem on F in absence of gravity and with zero contact angle. We show some examples of facets for which it is possible, even without the strict calibrability assumption, to build one of these vector fields. The construction provides, at least for convex facets of class C^{1,1}, the solution of the total variation flow starting at 1_F.

1 aAmato, Stefano1 aTealdi, Lucia1 aBellettini, Giovanni uhttp://urania.sissa.it/xmlui/handle/1963/3448100522nas a2200133 4500008004100000022001400041245015400055210006900209300001400278490000700292100001900299700002200318856004800340 2015 eng d a0176-427600aAsymptotics of orthogonal polynomials with complex varying quartic weight: global structure, critical point behavior and the first Painlevé equation0 aAsymptotics of orthogonal polynomials with complex varying quart a529–5870 v411 aBertola, Marco1 aTovbis, Alexander uhttp://dx.doi.org/10.1007/s00365-015-9288-001482nas a2200133 4500008004100000245013000041210007100171260001300242520098000255100002401235700001701259700002101276856005101297 2014 en d00aAn Abstract Nash–Moser Theorem and Quasi-Periodic Solutions for NLW and NLS on Compact Lie Groups and Homogeneous Manifolds0 aAbstract Nash–Moser Theorem and QuasiPeriodic Solutions for NLW bSpringer3 aWe prove an abstract implicit function theorem with parameters for smooth operators defined on scales of sequence spaces, modeled for the search of quasi-periodic solutions of PDEs. The tame estimates required for the inverse linearised operators at each step of the iterative scheme are deduced via a multiscale inductive argument. The Cantor-like set of parameters where the solution exists is defined in a non inductive way. This formulation completely decouples the iterative scheme from the measure theoretical analysis of the parameters where the small divisors non-resonance conditions are verified. As an application, we deduce the existence of quasi-periodic solutions for forced NLW and NLS equations on any compact Lie group or manifold which is homogeneous with respect to a compact Lie group, extending previous results valid only for tori. A basic tool of harmonic analysis is the highest weight theory for the irreducible representations of compact Lie groups.1 aBerti, Massimiliano1 aCorsi, Livia1 aProcesi, Michela uhttp://urania.sissa.it/xmlui/handle/1963/3465101483nas a2200121 4500008004100000245005900041210005900100260005900159520105100218100002201269700001901291856005101310 2014 en d00aAchieving unanimous opinions in signed social networks0 aAchieving unanimous opinions in signed social networks bInstitute of Electrical and Electronics Engineers Inc.3 aBeing able to predict the outcome of an opinion forming process is an important problem in social network theory. However, even for linear dynamics, this becomes a difficult task as soon as non-cooperative interactions are taken into account. Such interactions are naturally modeled as negative weights on the adjacency matrix of the social network. In this paper we show how the Perron-Frobenius theorem can be used for this task also beyond its standard formulation for cooperative systems. In particular we show how it is possible to associate the achievement of unanimous opinions with the existence of invariant cones properly contained in the positive orthant. These cases correspond to signed adjacency matrices having the eventual positivity property, i.e., such that in sufficiently high powers all negative entries have disappeared. More generally, we show how for social networks the achievement of a, possibily non-unanimous, opinion can be associated to the existence of an invariant cone fully contained in one of the orthants of n.1 aAltafini, Claudio1 aLini, Gabriele uhttp://urania.sissa.it/xmlui/handle/1963/3493500499nas a2200145 4500008004100000022001400041245009200055210006900147300001600216490000700232100002100239700002900260700002200289856004200311 2014 eng d a0272-497900aAdaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems0 aAdaptive discontinuous Galerkin methods for nonstationary convec a1578–15970 v341 aCangiani, Andrea1 aGeorgoulis, Emmanuil, H.1 aMetcalfe, Stephen uhttps://doi.org/10.1093/imanum/drt05201209nas a2200133 4500008004100000245010300041210006900144260001000213520075500223100002100978700002000999700002001019856003601039 2014 eng d00aAdler-Gelfand-Dickey approach to classical W-algebras within the theory of Poisson vertex algebras0 aAdlerGelfandDickey approach to classical Walgebras within the th bSISSA3 aWe put the Adler-Gelfand-Dickey approach to classical W-algebras in the framework of Poisson vertex algebras. We show how to recover the bi-Poisson structure of the KP hierarchy, together with its generalizations and reduction to the N-th KdV hierarchy, using the formal distribution calculus and the lambda-bracket formalism. We apply the Lenard-Magri scheme to prove integrability of the corresponding hierarchies. We also give a simple proof of a theorem of Kupershmidt and Wilson in this framework. Based on this approach, we generalize all these results to the matrix case. In particular, we find (non-local) bi-Poisson structures of the matrix KP and the matrix N-th KdV hierarchies, and we prove integrability of the N-th matrix KdV hierarchy.1 aDe Sole, Alberto1 aKac, Victor, G.1 aValeri, Daniele uhttp://hdl.handle.net/1963/724200836nas a2200121 4500008004100000245009000041210007300131260001300204520040500217100001600622700002500638856005100663 2014 en d00aApproximate Hermitian–Yang–Mills structures on semistable principal Higgs bundles0 aApproximate Hermitian–Yang–Mills structures on semistable princi bSpringer3 aWe generalize the Hitchin-Kobayashi correspondence between semistability and the existence of approximate Hermitian-Yang-Mills structures to the case of principal Higgs bundles. We prove that a principal Higgs bundle on a compact Kaehler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aGrana-Otero, Beatriz uhttp://urania.sissa.it/xmlui/handle/1963/3464500747nas a2200121 4500008004100000245006900041210006700110260003200177520032200209100001600531700002700547856005100574 2014 en d00aApproximate Hitchin-Kobayashi correspondence for Higgs G-bundles0 aApproximate HitchinKobayashi correspondence for Higgs Gbundles bWorld Scientific Publishing3 aWe announce a result about the extension of the Hitchin-Kobayashi correspondence to principal Higgs bundles. A principal Higgs bundle on a compact Kähler manifold, with structure group a connected linear algebraic reductive group, is semistable if and only if it admits an approximate Hermitian-Yang-Mills structure.1 aBruzzo, Ugo1 aOtero, Beatriz, Graña uhttp://urania.sissa.it/xmlui/handle/1963/3509501521nas a2200133 4500008004100000245009100041210006900132260001000201520106100211653003701272100002001309700002201329856003601351 2013 en d00aAmbrosio-Tortorelli approximation of cohesive fracture models in linearized elasticity0 aAmbrosioTortorelli approximation of cohesive fracture models in bSISSA3 aWe provide an approximation result in the sense of $\Gamma$-convergence for cohesive fracture energies of the form \[ \int_\Omega \mathscr{Q}_1(e(u))\,dx+a\,\mathcal{H}^{n-1}(J_u)+b\,\int_{J_u}\mathscr{Q}_0^{1/2}([u]\odot\nu_u)\,d\mathcal{H}^{n-1}, \] where $\Omega\subset{\mathbb R}^n$ is a bounded open set with Lipschitz boundary, $\mathscr{Q}_0$ and $\mathscr{Q}_1$ are coercive quadratic forms on ${\mathbb M}^{n\times n}_{sym}$, $a,\,b$ are positive constants, and $u$ runs in the space of fields $SBD^2(\Omega)$ , i.e., it's a special field with bounded deformation such that its symmetric gradient $e(u)$ is square integrable, and its jump set $J_u$ has finite $(n-1)$-Hausdorff measure in ${\mathbb R}^n$. The approximation is performed by means of Ambrosio-Tortorelli type elliptic regularizations, the prototype example being \[ \int_\Omega\Big(v|e(u)|^2+\frac{(1-v)^2}{\varepsilon}+{\gamma\,\varepsilon}|\nabla v|^2\Big)\,dx, \] where $(u,v)\in H^1(\Omega,{\mathbb R}^n){\times} H^1(\Omega)$, $\varepsilon\leq v\leq 1$ and $\gamma>0$.

10aFunctions of bounded deformation1 aFocardi, Matteo1 aIurlano, Flaviana uhttp://hdl.handle.net/1963/661501048nas a2200145 4500008004100000245010400041210006900145260001300214520050500227653007400732100002100806700001900827700002000846856003600866 2013 en d00aAnalytical validation of a continuum model for epitaxial growth with elasticity on vicinal surfaces0 aAnalytical validation of a continuum model for epitaxial growth bSpringer3 aIn this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].10asingular nonlinear parabolic equations, Hilbert transform, thin films1 aDal Maso, Gianni1 aFonseca, Irene1 aLeoni, Giovanni uhttp://hdl.handle.net/1963/724500531nas a2200109 4500008004100000245011300041210006900154260001000223653003700233100002200270856012900292 2013 en d00aAn Approximation Result for Generalised Functions of Bounded Deformation and Applications to Damage Problems0 aApproximation Result for Generalised Functions of Bounded Deform bSISSA10aFunctions of bounded deformation1 aIurlano, Flaviana uhttps://www.math.sissa.it/publication/approximation-result-generalised-functions-bounded-deformation-and-applications-damage01539nas a2200121 4500008004100000245009200041210006900133260005100202520107800253100001701331700001801348856005101366 2013 en d00aAsymptotics of the first Laplace eigenvalue with Dirichlet regions of prescribed length0 aAsymptotics of the first Laplace eigenvalue with Dirichlet regio bSociety for Industrial and Applied Mathematics3 aWe consider the problem of maximizing the first eigenvalue of the $p$-Laplacian (possibly with nonconstant coefficients) over a fixed domain $\Omega$, with Dirichlet conditions along $\partial\Omega$ and along a supplementary set $\Sigma$, which is the unknown of the optimization problem. The set $\Sigma$, which plays the role of a supplementary stiffening rib for a membrane $\Omega$, is a compact connected set (e.g., a curve or a connected system of curves) that can be placed anywhere in $\overline{\Omega}$ and is subject to the constraint of an upper bound $L$ to its total length (one-dimensional Hausdorff measure). This upper bound prevents $\Sigma$ from spreading throughout $\Omega$ and makes the problem well-posed. We investigate the behavior of optimal sets $\Sigma_L$ as $L\to\infty$ via $\Gamma$-convergence, and we explicitly construct certain asymptotically optimal configurations. We also study the behavior as $p\to\infty$ with $L$ fixed, finding connections with maximum-distance problems related to the principal frequency of the $\infty$-Laplacian.1 aTilli, Paolo1 aZucco, Davide uhttp://urania.sissa.it/xmlui/handle/1963/3514100882nas a2200133 4500008004100000245004600041210004600087260001000133520050000143100002600643700002100669700002200690856003600712 2013 en d00aAttainment results for nematic elastomers0 aAttainment results for nematic elastomers bSISSA3 aWe consider a class of non-quasiconvex frame indifferent energy densities which includes Ogden-type energy densities for nematic elastomers. For the corresponding geometrically linear problem we provide an explicit minimizer of the energy functional satisfying a nontrivial boundary condition. Other attainment results, both for the nonlinear and the linearized model, are obtained by using the theory of convex integration introduced by Mueller and Sverak in the context of crystalline solids.1 aAgostiniani, Virginia1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/717400868nas a2200145 4500008004100000245004700041210004400088260004800132520037400180100002100554700002100575700002500596700002200621856007900643 2012 en d00aAsymptotics of the s-perimeter as s →0 0 aAsymptotics of the sperimeter as s →0 bAmerican Institute of Mathematical Sciences3 aWe deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.

1 aDipierro, Serena1 aFigalli, Alessio1 aPalatucci, Giampiero1 aValdinoci, Enrico uhttps://www.math.sissa.it/publication/asymptotics-s-perimeter-s-%E2%86%92001400nas a2200169 4500008004100000245009000041210006900131260005000200520083200250100001401082700001801096700001501114700002201129700002201151700002101173856003601194 2011 en d00aAdaptation as a genome-wide autoregulatory principle in the stress response of yeast.0 aAdaptation as a genomewide autoregulatory principle in the stres bThe Institution of Engineering and Technology3 aThe gene expression response of yeast to various types of stresses/perturbations shows a common functional and dynamical pattern for the vast majority of genes, characterised by a quick transient peak (affecting primarily short genes) followed by a return to the pre-stimulus level. Kinetically, this process of adaptation following the transient excursion can be modelled using a genome-wide autoregulatory mechanism by means of which yeast aims at maintaining a preferential concentration in its mRNA levels. The resulting feedback system explains well the different time constants observable in the transient response, while being in agreement with all the known experimental dynamical features. For example, it suggests that a very rapid transient can be induced also by a slowly varying concentration of the gene products.1 aEduati, F1 aDi Camillo, B1 aToffolo, G1 aAltafini, Claudio1 aDe Palo, Giovanna1 aZampieri, Mattia uhttp://hdl.handle.net/1963/510600665nas a2200109 4500008004100000245007400041210007100115260001900186520029300205100002100498856003600519 2011 en d00aAn asymptotic reduction of a Painlevé VI equation to a Painlevé III0 aasymptotic reduction of a Painlevé VI equation to a Painlevé III bIOP Publishing3 aWhen the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents.1 aGuzzetti, Davide uhttp://hdl.handle.net/1963/512400772nas a2200157 4500008004300000245008600043210007000129260003400199520023700233653003600470100001900506700002200525700001600547700001500563856003600578 2011 en_Ud 00aAxial symmetry of some steady state solutions to nonlinear Schrödinger equations0 aAxial symmetry of some steady state solutions to nonlinear Schrö bAmerican Mathematical Society3 aIn this note, we show the axial symmetry of steady state solutions of nonlinear Schrodinger equations when the exponent of the nonlinearity is between the critical Sobolev exponent of n dimensional space and n - 1 dimensional space.10aNonlinear Schrödinger equation1 aGui, Changfeng1 aMalchiodi, Andrea1 aXu, Haoyuan1 aYang, Paul uhttp://hdl.handle.net/1963/410002010nas a2200385 4500008004100000022001300041245007600054210006900130300001200199490000700211520082800218653001601046653002101062653002301083653002101106653003001127653001901157653002201176653002501198653002701223653001801250653001801268653002401286653002801310653002201338653002201360653002401382653001901406653001201425653001901437100002401456700002001480700002101500856010301521 2010 eng d a0294144900aAn abstract Nash-Moser theorem with parameters and applications to PDEs0 aabstract NashMoser theorem with parameters and applications to P a377-3990 v273 aWe prove an abstract Nash-Moser implicit function theorem with parameters which covers the applications to the existence of finite dimensional, differentiable, invariant tori of Hamiltonian PDEs with merely differentiable nonlinearities. The main new feature of the abstract iterative scheme is that the linearized operators, in a neighborhood of the expected solution, are invertible, and satisfy the "tame" estimates, only for proper subsets of the parameters. As an application we show the existence of periodic solutions of nonlinear wave equations on Riemannian Zoll manifolds. A point of interest is that, in presence of possibly very large "clusters of small divisors", due to resonance phenomena, it is more natural to expect solutions with only Sobolev regularity. © 2009 Elsevier Masson SAS. All rights reserved.10aAbstracting10aAircraft engines10aFinite dimensional10aHamiltonian PDEs10aImplicit function theorem10aInvariant tori10aIterative schemes10aLinearized operators10aMathematical operators10aMoser theorem10aNon-Linearity10aNonlinear equations10aNonlinear wave equation10aPeriodic solution10aPoint of interest10aResonance phenomena10aSmall divisors10aSobolev10aWave equations1 aBerti, Massimiliano1 aBolle, Philippe1 aProcesi, Michela uhttps://www.math.sissa.it/publication/abstract-nash-moser-theorem-parameters-and-applications-pdes00340nas a2200097 4500008004100000245006800041210006700109260001000176100002000186856003600206 2010 en d00aAlmost-Riemannian Geometry from a Control Theoretical Viewpoint0 aAlmostRiemannian Geometry from a Control Theoretical Viewpoint bSISSA1 aGhezzi, Roberta uhttp://hdl.handle.net/1963/470500564nas a2200109 4500008004100000245005700041210005700098260001000155520022800165100002500393856003600418 2010 en d00aAspects of Quantum Field Theory on Quantum Spacetime0 aAspects of Quantum Field Theory on Quantum Spacetime bSISSA3 aWe provide a minimal, self-contained introduction to the covariant DFR flat\\r\\nquantum spacetime, and to some partial results for the corresponding quantum field theory. Explicit equations are given in the Dirac notation.1 aPiacitelli, Gherardo uhttp://hdl.handle.net/1963/417100988nas a2200133 4500008004100000022001400041245012300055210007000178300001600248490000800264520048400272100002700756856007100783 2008 eng d a0022-039600aAsymptotic evolution for the semiclassical nonlinear Schrödinger equation in presence of electric and magnetic fields0 aAsymptotic evolution for the semiclassical nonlinear Schrödinger a2566 - 25840 v2453 aIn this paper we study the semiclassical limit for the solutions of a subcritical focusing NLS with electric and magnetic potentials. We consider in particular the Cauchy problem for initial data close to solitons and show that, when the Planck constant goes to zero, the motion shadows that of a classical particle. Several works were devoted to the case of standing waves: differently from these we show that, in the dynamic version, the Lorentz force appears crucially.

1 aSelvitella, Alessandro uhttp://www.sciencedirect.com/science/article/pii/S002203960800243X00645nas a2200121 4500008004300000245011200043210006900155520019600224100002300420700002200443700002200465856003600487 2007 en_Ud 00aAsymptotic behaviour of smooth solutions for partially dissipative hyperbolic systems with a convex entropy0 aAsymptotic behaviour of smooth solutions for partially dissipati3 aWe study the asymptotic time behavior of global smooth solutions to general entropy dissipative hyperbolic systems of balance law in m space dimensions, under the Shizuta-Kawashima condition.1 aBianchini, Stefano1 aHanouzet, Bernard1 aNatalini, Roberto uhttp://hdl.handle.net/1963/178000925nas a2200121 4500008004100000245012500041210006900166260004700235520035300282100002100635700002100656856012600677 2007 en d00aThe Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics0 aAsymptotic Behaviour of the Fourier Transforms of Orthogonal Pol b2007 Birkh¨auser Verlag Basel/Switzerland3 aWe study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed1 aGuzzetti, Davide1 aMantica, Giorgio uhttps://www.math.sissa.it/publication/asymptotic-behaviour-fourier-transforms-orthogonal-polynomials-ii-lifs-measures-and01700nas a2200121 4500008004300000245004200043210004200085520136200127100002101489700001601510700001601526856003601542 2007 en_Ud 00aAsymptotic variational wave equations0 aAsymptotic variational wave equations3 aWe investigate the equation $(u_t + (f(u))_x)_x = f\\\'\\\'(u) (u_x)^2/2$ where $f(u)$ is a given smooth function. Typically $f(u)= u^2/2$ or $u^3/3$. This equation models unidirectional and weakly nonlinear waves for the variational wave equation $u_{tt} - c(u) (c(u)u_x)_x =0$ which models some liquid crystals with a natural sinusoidal $c$. The equation itself is also the Euler-Lagrange equation of a variational problem. Two natural classes of solutions can be associated with this equation. A conservative solution will preserve its energy in time, while a dissipative weak solution loses energy at the time when singularities appear. Conservative solutions are globally defined, forward and backward in time, and preserve interesting geometric features, such as the Hamiltonian structure. On the other hand, dissipative solutions appear to be more natural from the physical point of view.\\nWe establish the well-posedness of the Cauchy problem within the class of conservative solutions, for initial data having finite energy and assuming that the flux function $f$ has Lipschitz continuous second-order derivative. In the case where $f$ is convex, the Cauchy problem is well-posed also within the class of dissipative solutions. However, when $f$ is not convex, we show that the dissipative solutions do not depend continuously on the initial data.1 aBressan, Alberto1 aPing, Zhang1 aYuxi, Zheng uhttp://hdl.handle.net/1963/218200859nas a2200109 4500008004300000245008400043210006900127520047200196100002200668700002300690856003600713 2006 en_Ud 00aAlmost Global Stochastic Feedback Stabilization of Conditional Quantum Dynamics0 aAlmost Global Stochastic Feedback Stabilization of Conditional Q3 aWe propose several parametrization-free solutions to the problem of quantum state reduction control by means of continuous measurement and smooth quantum feedback. In particular, we design a feedback law for which almost global stochastic feedback stabilization can be proved analytically by means of Lyapunov techinques. This synthesis arises very naturally from the physics of the problem, as it relies on the variance associated with the quantum filtering process.1 aAltafini, Claudio1 aTicozzi, Francesco uhttp://hdl.handle.net/1963/172700611nas a2200109 4500008004300000245006500043210006200108520025700170100001900427700001900446856003600465 2006 en_Ud 00aAn artificial viscosity approach to quasistatic crack growth0 aartificial viscosity approach to quasistatic crack growth3 aWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\\\\epsilon$-gradient flow of the energy functional, as the \\\"viscosity\\\" parameter $\\\\epsilon$ tends to zero.1 aToader, Rodica1 aZanini, Chiara uhttp://hdl.handle.net/1963/185000897nas a2200121 4500008004300000245008900043210006900132260002400201520047200225100002000697700002200717856003600739 2005 en_Ud 00aAsymptotic Morse theory for the equation $\\\\Delta v=2v\\\\sb x\\\\wedge v\\\\sb y$0 aAsymptotic Morse theory for the equation Delta v2vsb xwedge vsb bInternational Press3 aGiven a smooth bounded domain ${\\\\O}\\\\subseteq \\\\R^2$, we consider the equation $\\\\D v = 2 v_x \\\\wedge v_y$ in $\\\\O$, where $v: {\\\\O}\\\\to \\\\R^3$. We prescribe Dirichlet boundary datum, and consider the case in which this datum converges to zero. An asymptotic study of the corresponding Euler functional is performed, analyzing multiple-bubbling phenomena. This allows us to settle a particular case of a question raised by H. Brezis and J.M. Coron.1 aChanillo, Sagun1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353301579nas a2200121 4500008004100000245007400041210006700115260001800182520117500200100001801375700002801393856003601421 2005 en d00aOn the attainable set for Temple class systems with boundary controls0 aattainable set for Temple class systems with boundary controls bSISSA Library3 aConsider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \\\\qquad u(0,x)=\\\\ov u(x), \\\\qquad {{array}{ll} &u(t,a)=\\\\widetilde u_a(t), \\\\noalign{\\\\smallskip} &u(t,b)=\\\\widetilde u_b(t), {array}. \\\\eqno(1) $$ on the domain $\\\\Omega =\\\\{(t,x)\\\\in\\\\R^2 : t\\\\geq 0, a \\\\le x\\\\leq b\\\\}.$ We study the mixed problem (1) from the point of view of control theory, taking the initial data $\\\\bar u$ fixed, and regarding the boundary data $\\\\widetilde u_a, \\\\widetilde u_b$ as control functions that vary in prescribed sets $\\\\U_a, \\\\U_b$, of $\\\\li$ boundary controls. In particular, we consider the family of configurations $$ \\\\A(T) \\\\doteq \\\\big\\\\{u(T,\\\\cdot); ~ u {\\\\rm is a sol. to} (1), \\\\quad \\\\widetilde u_a\\\\in \\\\U_a, \\\\widetilde u_b \\\\in \\\\U_b \\\\big\\\\} $$ that can be attained by the system at a given time $T>0$, and we give a description of the attainable set $\\\\A(T)$ in terms of suitable Oleinik-type conditions. We also establish closure and compactness of the set $\\\\A(T)$ in the $lu$ topology.1 aAncona, Fabio1 aCoclite, Giuseppe Maria uhttp://hdl.handle.net/1963/158100665nas a2200097 4500008004300000245004600043210004300089520037900132100002000511856003600531 2004 en_Ud 00aOn almost duality for Frobenius manifolds0 aalmost duality for Frobenius manifolds3 aWe present a universal construction of almost duality for Frobenius manifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We illustrate the general considerations by examples from the singularity theory, mirror symmetry, the theory of Coxeter groups and Shephard groups, from the Seiberg - Witten duality.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/254301230nas a2200109 4500008004100000245005200041210004900093260001000142520091200152100002001064856003601084 2004 en d00aOn analytic families of invariant tori for PDEs0 aanalytic families of invariant tori for PDEs bSISSA3 aWe propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/647401188nas a2200121 4500008004100000245012000041210006900161260001800230520074100248100002100989700002001010856003601030 2004 en d00aAsymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains0 aAsymptotic behaviour and correctors for linear Dirichlet problem bSISSA Library3 aWe consider a sequence of Dirichlet problems in varying domains (or, more generally, of relaxed Dirichlet problems involving measures in M_0) for second order linear elliptic operators in divergence form with varying matrices of coefficients. When the matrices H-converge to a matrix A^0, we prove that there exist a subsequence and a measure mu^0 in M_0 such that the limit problem is the relaxed Dirichlet problem corresponding to A^0 and mu^0. We also prove a corrector result which provides an explicit approximation of the solutions in the H^1-norm, and which is obtained by multiplying the corrector for the H-converging matrices by some special test function which depends both on the varying matrices and on the varying domains.1 aDal Maso, Gianni1 aMurat, Francois uhttp://hdl.handle.net/1963/161100496nas a2200109 4500008004100000245017800041210006900219260001800288100002100306700002300327856003600350 2003 en d00aAutonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations0 aAutonomous integral functionals with discontinous nonconvex inte bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/162500399nas a2200109 4500008004100000245007900041210006900120260001800189100002300207700002300230856003600253 2002 en d00aAdmissible Riemann solvers for genuinely nonlinear P-systems of mixed type0 aAdmissible Riemann solvers for genuinely nonlinear Psystems of m bSISSA Library1 aMercier, Jean-Marc1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/149100800nas a2200109 4500008004100000245005300041210005200094260003600146520039600182100002400578856008800602 2002 en d00aArnold diffusion: a functional analysis approach0 aArnold diffusion a functional analysis approach bNatsīonal. Akad. Nauk Ukraïni3 aWe present, in the context of nearly integrable Hamiltonian systems, a functional analysis approach to study the “splitting of the whiskers” and the “shadowing problem” developed in collaboration with P. Bolle in the recent papers [1] and [2] . This method is applied to the problem of Arnold diffusion for nearly integrable partially isochronous systems improving known results.1 aBerti, Massimiliano uhttps://www.math.sissa.it/publication/arnold-diffusion-functional-analysis-approach00715nas a2200109 4500008004100000245007200041210006900113260001800182520034700200100002200547856003600569 2001 en d00aAdiabatic limits of closed orbits for some Newtonian systems in R-n0 aAdiabatic limits of closed orbits for some Newtonian systems in bSISSA Library3 aWe deal with a Newtonian system like x\\\'\\\' + V\\\'(x) = 0. We suppose that V: \\\\R^n \\\\to \\\\R possesses an (n-1)-dimensional compact manifold M of critical points, and we prove the existence of arbitrarity slow periodic orbits. When the period tends to infinity these orbits, rescaled in time, converge to some closed geodesics on M.1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/151100351nas a2200109 4500008004100000245005300041210005300094260001800147100001700165700002300182856003600205 2000 en d00aAbnormal extremals for minimum time on the plane0 aAbnormal extremals for minimum time on the plane bSISSA Library1 aBoscain, Ugo1 aPiccoli, Benedetto uhttp://hdl.handle.net/1963/150800394nas a2200109 4500008004100000245007600041210006900117260001800186100002400204700002000228856003600248 2000 en d00aArnold's Diffusion in nearly integrable isochronous Hamiltonian systems0 aArnolds Diffusion in nearly integrable isochronous Hamiltonian s bSISSA Library1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/155400397nas a2200121 4500008004100000245006300041210005500104260001800159100002200177700001800199700002200217856003600239 2000 en d00aA(SLq(2)) at roots of unity is a free module over A(SL(2))0 aASLq2 at roots of unity is a free module over ASL2 bSISSA Library1 aDabrowski, Ludwik1 aReina, Cesare1 aZampa, Alessandro uhttp://hdl.handle.net/1963/150000595nas a2200109 4500008004100000245010900041210006900150260002300219520018900242100001800431856003600449 1999 en d00aThe anisotropy introduced by the mesh in the finite element approximation of the Mumford-Shah functional0 aanisotropy introduced by the mesh in the finite element approxim bTaylor and Francis3 aWe compute explicitly the anisotropy effect in the H1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations.1 aNegri, Matteo uhttp://hdl.handle.net/1963/127600329nas a2200097 4500008004100000245006300041210006200104260001000166100001900176856003600195 1999 en d00aApproximation, Stability and control for Conservation Laws0 aApproximation Stability and control for Conservation Laws bSISSA1 aMarson, Andrea uhttp://hdl.handle.net/1963/550000405nas a2200109 4500008004100000020001400041245009200055210006900147100002100216700002200237856003600259 1999 en d a1618-189100aAsymptotic behaviour of nonlinear elliptic higher order equations in perforated domains0 aAsymptotic behaviour of nonlinear elliptic higher order equation1 aDal Maso, Gianni1 aSkrypnik, Igor V. uhttp://hdl.handle.net/1963/643300388nas a2200109 4500008004100000245007500041210007000116260001000186653002600196100002000222856003600242 1998 en d00aAlgebraic Solutions to the Painlevé-VI Equation and Reflection Groups0 aAlgebraic Solutions to the PainlevéVI Equation and Reflection Gr bSISSA10aPainlevé VI equation1 aMazzocco, Marta uhttp://hdl.handle.net/1963/557400395nas a2200109 4500008004100000245007800041210006900119260001800188100002100206700002200227856003600249 1998 en d00aAsymptotic behavior of nonlinear Dirichlet problems in perforated domains0 aAsymptotic behavior of nonlinear Dirichlet problems in perforate bSISSA Library1 aDal Maso, Gianni1 aSkrypnik, Igor V. uhttp://hdl.handle.net/1963/106400368nas a2200109 4500008004300000245006800043210006600111260001000177100001500187700002000202856003600222 1994 en_Ud 00aAlgebraic-geometrical Darboux coordinates in R-matrix formalism0 aAlgebraicgeometrical Darboux coordinates in Rmatrix formalism bSISSA1 aDiener, P.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/365500392nas a2200109 4500008004100000245008000041210006900121260001000190653002400200100002200224856003600246 1994 en d00aAnalysis of Singularity Structures for Quasi-Integrable Hamiltonian Systems0 aAnalysis of Singularity Structures for QuasiIntegrable Hamiltoni bSISSA10aHamiltonian systems1 aAbenda, Simonetta uhttp://hdl.handle.net/1963/568500379nas a2200109 4500008004100000245006900041210006900110260001000179653002300189100002100212856003600233 1994 en d00aAsymptotic Behaviour of Dirichlet Problems in Perforated Domains0 aAsymptotic Behaviour of Dirichlet Problems in Perforated Domains bSISSA10aDirichlet problems1 aGarroni, Adriana uhttp://hdl.handle.net/1963/571400354nas a2200109 4500008004100000245005500041210005500096260001800151100002000169700002000189856003500209 1990 en d00aAlgebraic differential calculus for gauge theories0 aAlgebraic differential calculus for gauge theories bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/89100407nas a2200109 4500008004100000245009300041210006900134260001800203100002100221700002000242856003500262 1989 en d00aAn approach to the thin obstacle problem for variational functionals depending on vector0 aapproach to the thin obstacle problem for variational functional bSISSA Library1 aDal Maso, Gianni1 aMusina, Roberta uhttp://hdl.handle.net/1963/80200397nas a2200109 4500008004100000245008400041210006900125260001800194100002000212700002000232856003500252 1988 en d00aAlgebraic reduction of the \\\'t Hooft-Polyakov monopole to the Dirac monopole.0 aAlgebraic reduction of the t HooftPolyakov monopole to the Dirac bSISSA Library1 aLandi, Giovanni1 aMarmo, Giuseppe uhttp://hdl.handle.net/1963/57800290nas a2200097 4500008004100000245004400041210004100085260001000126100002000136856003600156 1988 en d00aAn Algebraic Setting for Gauge Theories0 aAlgebraic Setting for Gauge Theories bSISSA1 aLandi, Giovanni uhttp://hdl.handle.net/1963/582800372nas a2200097 4500008004100000245008700041210006900128260001800197100002400215856003500239 1983 en d00aOn the asymptotic behaviour of solutions to Pazy\\\'s class of evolution equations0 aasymptotic behaviour of solutions to Pazys class of evolution eq bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/276