We study the blow-up behavior of minimizing sequences for the singular Moser–Trudinger functional on compact surfaces. Assuming non-existence of minimum points, we give an estimate for the infimum value of the functional. This result can be applied to give sharp Onofri-type inequalities on the sphere in the presence of at most two singularities.

1 aMancini, Gabriele uhttps://www.math.sissa.it/publication/onofri-type-inequalities-singular-liouville-equations01596nas a2200133 4500008004100000245010900041210006900150260001000219520113200229100002101361700002201382700002201404856003601426 2013 en d00aOne-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls0 aOnedimensional swimmers in viscous fluids dynamics controllabili bSISSA3 aIn this paper we study a mathematical model of one-dimensional swimmers performing a planar motion while fully immersed in a viscous fluid. The swimmers are assumed to be of small size, and all inertial effects are neglected. Hydrodynamic interactions are treated in a simplified way, using the local drag approximation of resistive force theory. We prove existence and uniqueness of the solution of the equations of motion driven by shape changes of the swimmer. Moreover, we prove a controllability result showing that given any pair of initial and final states, there exists a history of shape changes such that the resulting motion takes the swimmer from the initial to the final state. We give a constructive proof, based on the composition of elementary maneuvers (straightening and its inverse, rotation, translation), each of which represents the solution of an interesting motion planning problem. Finally, we prove the existence of solutions for the optimal control problem of finding, among the histories of shape changes taking the swimmer from an initial to a final state, the one of minimal energetic cost.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/646701684nas a2200157 4500008004100000245004700041210004600088260001300134300001200147490000700159520120600166653002501372100002601397700002201423856008101445 2012 en d00aOgden-type energies for nematic elastomers0 aOgdentype energies for nematic elastomers bElsevier a402-4120 v473 aOgden-type extensions of the free-energy densities currently used to model the mechanical behavior of nematic elastomers are proposed and analyzed. Based on a multiplicative decomposition of the deformation gradient into an elastic and a spontaneous or remanent part, they provide a suitable framework to study the stiffening response at high imposed stretches. Geometrically linear versions of the models (Taylor expansions at order two) are provided and discussed. These small strain theories provide a clear illustration of the geometric structure of the underlying energy landscape (the energy grows quadratically with the distance from a non-convex set of spontaneous strains or energy wells). The comparison between small strain and finite deformation theories may also be useful in the opposite direction, inspiring finite deformation generalizations of small strain theories currently used in the mechanics of active and phase-transforming materials. The energy well structure makes the free-energy densities non-convex. Explicit quasi-convex envelopes are provided, and applied to compute the stiffening response of a specimen tested in plane strain extension experiments (pure shear).

10aNonlinear elasticity1 aAgostiniani, Virginia1 aDeSimone, Antonio uhttps://www.math.sissa.it/publication/ogden-type-energies-nematic-elastomers00559nas a2200121 4500008004100000245012000041210006900161260003700230300001400267490000700281100002300288856012600311 2012 eng d00aOne-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations0 aOnesigned harmonic solutions and signchanging subharmonic soluti bAdvanced Nonlinear Studies, Inc. a445–4630 v121 aBoscaggin, Alberto uhttps://www.math.sissa.it/publication/one-signed-harmonic-solutions-and-sign-changing-subharmonic-solutions-scalar-second00376nas a2200109 4500008004100000245007700041210006900118300001200187490000700199100002200206856003800228 2012 eng d00aOptimal Transport with Branching Distance Costs and the Obstacle Problem0 aOptimal Transport with Branching Distance Costs and the Obstacle a454-4820 v441 aCavalletti, Fabio uhttps://doi.org/10.1137/10080143300449nas a2200109 4500008004300000245005100043210005100094260003400145520010000179100002400279856003600303 2011 en_Ud 00aOsservazioni sui teoremi di inversione globale0 aOsservazioni sui teoremi di inversione globale bEuropean Mathematical Society3 aSome global inversion theorems with applications to semilinear elliptic equation are discussed.1 aAmbrosetti, Antonio uhttp://hdl.handle.net/1963/406801159nas a2200121 4500008004300000245006200043210005800105260001300163520078100176100002300957700002100980856003601001 2010 en_Ud 00aOn optimality of c-cyclically monotone transference plans0 aoptimality of ccyclically monotone transference plans bElsevier3 aAbstract. This note deals with the equivalence between the optimality of a transport plan for the Monge-Kantorovich problem and the condition of c-cyclical monotonicity, as an outcome of the construction in [7]. We emphasize the measurability assumption on the hidden structure of linear preorder, applied also to extremality and uniqueness problems. Resume. Dans la presente note nous decrivons brievement la construction introduite dans [7] a propos de l\\\'equivalence entre l\\\'optimalite d\\\'un plan de transport pour le probleme de Monge-Kantorovich et la condition de monotonie c-cyclique ainsi que d\\\'autres sujets que cela nous amene a aborder. Nous souhaitons mettre en evidence l\\\'hypothese de mesurabilite sur la structure sous-jacente de pre-ordre lineaire.1 aBianchini, Stefano1 aCaravenna, Laura uhttp://hdl.handle.net/1963/402301187nas a2200145 4500008004300000245004000043210004000083520078100123100002300904700002200927700001700949700002000966700001900986856003601005 2010 en_Ud 00aOptimally swimming Stokesian Robots0 aOptimally swimming Stokesian Robots3 aWe study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.1 aAlouges, François1 aDeSimone, Antonio1 aHeltai, Luca1 aLefebvre, Aline1 aMerlet, Benoit uhttp://hdl.handle.net/1963/392901018nas a2200109 4500008004300000245005800043210005800101520067400159100002500833700001400858856003600872 2009 en_Ud 00aOptimal transportation under nonholonomic constraints0 aOptimal transportation under nonholonomic constraints3 aWe study the Monge\\\'s optimal transportation problem where the cost is given by optimal control cost. We prove the existence and uniqueness of optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the measures and most importantly the absent of sharp abnormal minimizers. In particular, this result is applicable in the case of subriemannian manifolds with a 2-generating distribution and cost given by d2, where d is the subriemannian distance. Also, we discuss some properties of the optimal plan when abnormal minimizers are present. Finally, we consider some examples of displacement interpolation in the case of Grushin plane.1 aAgrachev, Andrei, A.1 aLee, Paul uhttp://hdl.handle.net/1963/217601131nas a2200133 4500008004300000245006500043210006400108260001300172520071100185100002300896700002200919700002000941856003600961 2008 en_Ud 00aOptimal Strokes for Low Reynolds Number Swimmers: An Example0 aOptimal Strokes for Low Reynolds Number Swimmers An Example bSpringer3 aSwimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901-062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).1 aAlouges, François1 aDeSimone, Antonio1 aLefebvre, Aline uhttp://hdl.handle.net/1963/400602183nas a2200133 4500008004300000245010900043210006900152520170600221100002101927700002001948700002301968700002201991856003602013 2008 en_Ud 00aOrigin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms0 aOrigin of CoExpression Patterns in Ecoli and Scerevisiae Emergin3 aBackground: The concept of reverse engineering a gene network, i.e., of inferring a genome-wide graph of putative genegene interactions from compendia of high throughput microarray data has been extensively used in the last few years to deduce/integrate/validate various types of \\\"physical\\\" networks of interactions among genes or gene products. Results: This paper gives a comprehensive overview of which of these networks emerge significantly when reverse engineering large collections of gene expression data for two model organisms, E.coli and S.cerevisiae, without any prior information. For the first organism the pattern of co-expression is shown to reflect in fine detail both the operonal structure of the DNA and the regulatory effects exerted by the gene products when co-participating in a protein complex. For the second organism we find that direct transcriptional control (e.g., transcription factor-binding site interactions) has little statistical significance in comparison to the other regulatory mechanisms (such as co-sharing a protein complex, colocalization on a metabolic pathway or compartment), which are however resolved at a lower level of detail than in E.coli. Conclusion: The gene co-expression patterns deduced from compendia of profiling experiments tend to unveil functional categories that are mainly associated to stable bindings rather than transient interactions. The inference power of this systematic analysis is substantially reduced when passing from E.coli to S.cerevisiae. This extensive analysis provides a way to describe the different complexity between the two organisms and discusses the critical limitations affecting this type of methodologies.1 aZampieri, Mattia1 aSoranzo, Nicola1 aBianchini, Daniele1 aAltafini, Claudio uhttp://hdl.handle.net/1963/272200982nas a2200109 4500008004300000245008000043210006900123520060400192100002100796700001900817856003600836 2005 en_Ud 00aAn Optimal Transportation Metric for Solutions of the Camassa-Holm Equation0 aOptimal Transportation Metric for Solutions of the CamassaHolm E3 aIn this paper we construct a global, continuous flow of solutions to the Camassa-Holm equation on the entire space H1. Our solutions are conservative, in the sense that the total energy int[(u2 + u2x) dx] remains a.e. constant in time. Our new approach is based on a distance functional J(u, v), defined in terms of an optimal transportation problem, which satisfies d dtJ(u(t), v(t)) ≤ κ · J(u(t), v(t)) for every couple of solutions. Using this new distance functional, we can construct arbitrary solutions as the uniform limit of multi-peakon solutions, and prove a general uniqueness result.1 aBressan, Alberto1 aFonte, Massimo uhttp://hdl.handle.net/1963/171900319nas a2200109 4500008004100000245004500041210004400086260001000130653001400140100001900154856003600173 2005 en d00aOrbifold Cohomology of ADE-singularities0 aOrbifold Cohomology of ADEsingularities bSISSA10aOrbifolds1 aPerroni, Fabio uhttp://hdl.handle.net/1963/529800423nas a2200121 4500008004100000245007600041210006900117260001800186100001700204700002400221700002000245856003600265 2002 en d00aAn optimal fast-diffusion variational method for non isochronous system0 aoptimal fastdiffusion variational method for non isochronous sys bSISSA Library1 aBiasco, Luca1 aBerti, Massimiliano1 aBolle, Philippe uhttp://hdl.handle.net/1963/157900446nas a2200121 4500008004100000245009900041210006900140260001800209100002400227700001700251700002000268856003600288 2002 en d00aOptimal stability and instability results for a class of nearly integrable Hamiltonian systems0 aOptimal stability and instability results for a class of nearly bSISSA Library1 aBerti, Massimiliano1 aBiasco, Luca1 aBolle, Philippe uhttp://hdl.handle.net/1963/159600990nas a2200121 4500008004300000245007000043210006900113260001300182520059800195100002100793700001800814856003600832 1999 en_Ud 00aOleinik type estimates and uniqueness for n x n conservation laws0 aOleinik type estimates and uniqueness for n x n conservation law bElsevier3 aLet $u_t+f(u)_x=0$ be a strictly hyperbolic $n\\\\times n$ system of conservation laws in one space dimension. Relying on the existence of a semigroup of solutions, we first establish the uniqueness of entropy admissible weak solutions to the Cauchy problem, under a mild assumption on the local oscillation of $u$ in a forward neighborhood of each point in the $t\\\\text{-}x$ plane. In turn, this yields the uniqueness of weak solutions which satisfy a decay estimate on positive waves of genuinely nonlinear families, thus extending a classical result proved by Oleĭnik in the scalar case.1 aBressan, Alberto1 aGoatin, Paola uhttp://hdl.handle.net/1963/337500349nas a2200097 4500008004100000245007000041210006300111260001800174100002400192856003500216 1982 en d00aOn the obstacle problem for strongly nonlinear elliptic equations0 aobstacle problem for strongly nonlinear elliptic equations bSISSA Library1 aVidossich, Giovanni uhttp://hdl.handle.net/1963/162