We study the blow-up behavior of minimizing sequences for the singular Moser{\textendash}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.

}, doi = {10.1007/s12220-015-9589-3}, author = {Gabriele Mancini} } @article {2013, title = {One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls}, number = {arXiv:1302.0901;}, year = {2013}, publisher = {SISSA}, abstract = {In 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.

}, url = {http://hdl.handle.net/1963/6467}, author = {Gianni Dal Maso and Antonio DeSimone and Marco Morandotti} } @article {2012, title = {Ogden-type energies for nematic elastomers}, journal = {International Journal of Non-Linear mechanics }, volume = {47}, year = {2012}, pages = {402-412}, publisher = {Elsevier}, abstract = {Ogden-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).

}, keywords = {Nonlinear elasticity}, doi = {10.1016/j.ijnonlinmec.2011.10.001}, author = {Virginia Agostiniani and Antonio DeSimone} } @article {boscaggin2012one, title = {One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations}, journal = {Advanced Nonlinear Studies}, volume = {12}, number = {3}, year = {2012}, pages = {445{\textendash}463}, publisher = {Advanced Nonlinear Studies, Inc.}, doi = {10.1515/ans-2012-0302}, author = {Alberto Boscaggin} } @article {doi:10.1137/100801433, title = {Optimal Transport with Branching Distance Costs and the Obstacle Problem}, journal = {SIAM Journal on Mathematical Analysis}, volume = {44}, number = {1}, year = {2012}, pages = {454-482}, doi = {10.1137/100801433}, url = {https://doi.org/10.1137/100801433}, author = {Fabio Cavalletti} } @article {2011, title = {Osservazioni sui teoremi di inversione globale}, journal = {Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15}, number = {SISSA;64/2010/M}, year = {2011}, publisher = {European Mathematical Society}, abstract = {Some global inversion theorems with applications to semilinear elliptic equation are discussed.}, doi = {10.4171/RLM/584}, url = {http://hdl.handle.net/1963/4068}, author = {Antonio Ambrosetti} } @article {2010, title = {On optimality of c-cyclically monotone transference plans}, journal = {Comptes Rendus Mathematique 348 (2010) 613-618}, year = {2010}, publisher = {Elsevier}, abstract = {Abstract. 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.}, doi = {10.1016/j.crma.2010.03.022}, url = {http://hdl.handle.net/1963/4023}, author = {Stefano Bianchini and Laura Caravenna} } @article {2010, title = {Optimally swimming Stokesian Robots}, number = {SISSA;54/2010/M}, year = {2010}, abstract = {We 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.}, url = {http://hdl.handle.net/1963/3929}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet} } @article {2009, title = {Optimal transportation under nonholonomic constraints}, journal = {Trans. Amer. Math. Soc. 361 (2009) 6019-6047}, number = {SISSA;68/2007/M}, year = {2009}, abstract = {We 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.}, doi = {10.1090/S0002-9947-09-04813-2}, url = {http://hdl.handle.net/1963/2176}, author = {Andrei A. Agrachev and Paul Lee} } @article {2008, title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example}, journal = {J. Nonlinear Sci. 18 (2008) 277-302}, year = {2008}, publisher = {Springer}, abstract = {Swimming, 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).}, doi = {10.1007/s00332-007-9013-7}, url = {http://hdl.handle.net/1963/4006}, author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre} } @article {2008, title = {Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms}, journal = {PLoS ONE 3 (2008) e2981}, year = {2008}, abstract = {Background: 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.}, doi = {10.1371/journal.pone.0002981}, url = {http://hdl.handle.net/1963/2722}, author = {Mattia Zampieri and Nicola Soranzo and Daniele Bianchini and Claudio Altafini} } @article {2005, title = {An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation}, number = {SISSA;27/2005/M}, year = {2005}, abstract = {In 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 {\textperiodcentered} 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.}, url = {http://hdl.handle.net/1963/1719}, author = {Alberto Bressan and Massimo Fonte} } @mastersthesis {2005, title = {Orbifold Cohomology of ADE-singularities}, year = {2005}, school = {SISSA}, keywords = {Orbifolds}, url = {http://hdl.handle.net/1963/5298}, author = {Fabio Perroni} } @article {2002, title = {An optimal fast-diffusion variational method for non isochronous system}, number = {SISSA;8/2002/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1579}, author = {Luca Biasco and Massimiliano Berti and Philippe Bolle} } @article {2002, title = {Optimal stability and instability results for a class of nearly integrable Hamiltonian systems}, journal = {Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84}, number = {SISSA;25/2002/M}, year = {2002}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/1596}, author = {Massimiliano Berti and Luca Biasco and Philippe Bolle} } @article {1999, title = {Oleinik type estimates and uniqueness for n x n conservation laws}, journal = {J. Differential Equations 156 (1999), no. 1, 26--49}, number = {SISSA;150/97/M}, year = {1999}, publisher = {Elsevier}, abstract = {Let $u_t+f(u)_x=0$ 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 Oleinik in the scalar case.}, doi = {10.1006/jdeq.1998.3606}, url = {http://hdl.handle.net/1963/3375}, author = {Alberto Bressan and Paola Goatin} } @article {1982, title = {On the obstacle problem for strongly nonlinear elliptic equations}, number = {SISSA;11/82/M}, year = {1982}, publisher = {SISSA Library}, url = {http://hdl.handle.net/1963/162}, author = {Giovanni Vidossich} }