The use of Cerami sequences in critical point theory.
Three solutions of a quasilinear elliptic problem near resonance
T-Periodic Solutions of Time Dependent Hamiltonian Systems with a Potential Vanishing at Infinity.
Traveling wave solutions of the heat flow of director fields
Two-scale convergence of a model for flow in a partially fissured medium.
Tzitzeica theory -- opportunity for reflection in mathematics.
Un théorème de prolongement pour l'opérateur « divergence »
Une justification de modèles de plaques viscoplastiques
Uniform convergence of a Galerkin-type method for a non-linear boundary value problem
Upper bounds for a class of energies containing a non-local term
In this paper we construct upper bounds for families of functionals of the formwhere Δ = div {u}. Particular cases of such functionals arise in Micromagnetics. We also use our technique to construct upper bounds for functionals that appear in a variational formulation of the method of vanishing viscosity for conservation laws.
Variational approach to dynamics of bright solitons in lossy optical fibers.
Variational Framework for Assessment of the Left Ventricle Motion
Impairment of left ventricular contractility due to cardiovascular diseases is reflected in left ventricle (LV) motion patterns. An abnormal change of torsion or long axis shortening LV values can help with the diagnosis and follow-up of LV dysfunction. Tagged Magnetic Resonance (TMR) is a widely spread medical imaging modality that allows estimation of the myocardial tissue local deformation. In this work, we introduce a novel variational framework for extracting the left ventricle dynamics from...
Variational methods in nonlinear problems
Variational principle for nonlinear Schrödinger equation with high nonlinearity.
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Vortices for a variational problem related to superconductivity
Vorticité dans les modèles de Ginzburg-Landau pour la supraconductivité
Wasserstein gradient flows from large deviations of many-particle limits
We study the Fokker–Planck equation as the many-particle limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the path-space rate functional, which characterises the large deviations from the expected trajectories, in such a way that the free energy appears explicitly. Next we use this formulation via the contraction principle to prove that the discrete time rate functional is asymptotically equivalent in the Gamma-convergence sense to the functional...
Weak solution for nonlinear degenerate elliptic problem with Dirichlet-type boundary condition in weighted Sobolev spaces
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
Weighted energy-dissipation functionals for gradient flows
We investigate a global-in-time variational approach to abstract evolution by means of the weighted energy-dissipation functionals proposed by Mielke and Ortiz [ESAIM: COCV14 (2008) 494–516]. In particular, we focus on gradient flows in Hilbert spaces. The main result is the convergence of minimizers and approximate minimizers of these functionals to the unique solution of the gradient flow. Sharp convergence rates are provided and the convergence analysis is combined with time-discretization....