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.

PB - Springer US U1 - 34668 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - One-dimensional swimmers in viscous fluids: dynamics, controllability, and existence of optimal controls Y1 - 2013 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -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.

PB - SISSA UR - http://hdl.handle.net/1963/6467 U1 - 6412 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - Ogden-type energies for nematic elastomers JF - International Journal of Non-Linear mechanics Y1 - 2012 A1 - Virginia Agostiniani A1 - Antonio DeSimone KW - Nonlinear elasticity AB -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).

PB - Elsevier VL - 47 IS - 2 U1 - 6971 U2 - Mathematics U4 - -1 ER - TY - JOUR T1 - One-signed harmonic solutions and sign-changing subharmonic solutions to scalar second order differential equations JF - Advanced Nonlinear Studies Y1 - 2012 A1 - Alberto Boscaggin PB - Advanced Nonlinear Studies, Inc. VL - 12 ER - TY - JOUR T1 - Optimal Transport with Branching Distance Costs and the Obstacle Problem JF - SIAM Journal on Mathematical Analysis Y1 - 2012 A1 - Fabio Cavalletti VL - 44 UR - https://doi.org/10.1137/100801433 ER - TY - JOUR T1 - Osservazioni sui teoremi di inversione globale JF - Rendiconti Lincei - Matematica e Applicazioni 22 (2011) 3-15 Y1 - 2011 A1 - Antonio Ambrosetti AB - Some global inversion theorems with applications to semilinear elliptic equation are discussed. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4068 U1 - 334 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On optimality of c-cyclically monotone transference plans JF - Comptes Rendus Mathematique 348 (2010) 613-618 Y1 - 2010 A1 - Stefano Bianchini A1 - Laura Caravenna AB - 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. PB - Elsevier UR - http://hdl.handle.net/1963/4023 U1 - 379 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - Optimally swimming Stokesian Robots Y1 - 2010 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai A1 - Aline Lefebvre A1 - Benoit Merlet AB - 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. UR - http://hdl.handle.net/1963/3929 U1 - 472 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal transportation under nonholonomic constraints JF - Trans. Amer. Math. Soc. 361 (2009) 6019-6047 Y1 - 2009 A1 - Andrei A. Agrachev A1 - Paul Lee AB - 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. UR - http://hdl.handle.net/1963/2176 U1 - 2068 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal Strokes for Low Reynolds Number Swimmers: An Example JF - J. Nonlinear Sci. 18 (2008) 277-302 Y1 - 2008 A1 - François Alouges A1 - Antonio DeSimone A1 - Aline Lefebvre AB - 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). PB - Springer UR - http://hdl.handle.net/1963/4006 U1 - 396 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Origin of Co-Expression Patterns in E.coli and S.cerevisiae Emerging from Reverse Engineering Algorithms JF - PLoS ONE 3 (2008) e2981 Y1 - 2008 A1 - Mattia Zampieri A1 - Nicola Soranzo A1 - Daniele Bianchini A1 - Claudio Altafini AB - 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. UR - http://hdl.handle.net/1963/2722 U1 - 1379 U2 - Physics U3 - Functional Analysis and Applications ER - TY - RPRT T1 - An Optimal Transportation Metric for Solutions of the Camassa-Holm Equation Y1 - 2005 A1 - Alberto Bressan A1 - Massimo Fonte AB - 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 · 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. JF - Methods Appl. Anal. 12 (2005) 191-219 UR - http://hdl.handle.net/1963/1719 U1 - 2432 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - THES T1 - Orbifold Cohomology of ADE-singularities Y1 - 2005 A1 - Fabio Perroni KW - Orbifolds PB - SISSA UR - http://hdl.handle.net/1963/5298 U1 - 5126 U2 - Mathematics U3 - Mathematical Physics U4 - -1 ER - TY - JOUR T1 - An optimal fast-diffusion variational method for non isochronous system Y1 - 2002 A1 - Luca Biasco A1 - Massimiliano Berti A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1579 U1 - 2539 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal stability and instability results for a class of nearly integrable Hamiltonian systems JF - Atti.Accad.Naz.Lincei Cl.Sci.Fis.Mat.Natur.Rend.Lincei (9) Mat.Appl.13(2002),no.2,77-84 Y1 - 2002 A1 - Massimiliano Berti A1 - Luca Biasco A1 - Philippe Bolle PB - SISSA Library UR - http://hdl.handle.net/1963/1596 U1 - 2522 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Oleinik type estimates and uniqueness for n x n conservation laws JF - J. Differential Equations 156 (1999), no. 1, 26--49 Y1 - 1999 A1 - Alberto Bressan A1 - Paola Goatin AB - 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 Oleĭnik in the scalar case. PB - Elsevier UR - http://hdl.handle.net/1963/3375 U1 - 955 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - On the obstacle problem for strongly nonlinear elliptic equations Y1 - 1982 A1 - Giovanni Vidossich PB - SISSA Library UR - http://hdl.handle.net/1963/162 U1 - 3805 U2 - Mathematics U3 - Functional Analysis and Applications ER -