Variational methods and linearization tools towards the spectral analysis of the -Laplacian, especially for the Fredholm alternative.
Variational methods for a resonant problem with the -Laplacian in .
Variational problems in domains with cusp points
The finite element analysis of linear elliptic problems in two-dimensional domains with cusp points (turning points) is presented. This analysis needs on one side a generalization of results concerning the existence and uniqueness of the solution of a constinuous elliptic variational problem in a domain the boundary of which is Lipschitz continuous and on the other side a presentation of a new finite element interpolation theorem and other new devices.
Variational problems on classes of rearrangements and multiple configurations for steady vortices
Variational problems with pointwise constraints on the derivatives.
Von Neumann analysis of linearized discrete Tzitzeica PDE.
Vortex dans les condensats de Bose Einstein
Vortex rings for the Gross-Pitaevskii equation
We provide a mathematical proof of the existence of traveling vortex rings solutions to the Gross–Pitaevskii (GP) equation in dimension . We also extend the asymptotic analysis of the free field Ginzburg–Landau equation to a larger class of equations, including the Ginzburg–Landau equation for superconductivity as well as the traveling wave equation for GP. In particular we rigorously derive a curvature equation for the concentration set (i.e. line vortices if ).
Vortices in Ginzburg-Landau equations.
Waves of Autocrine Signaling in Patterned Epithelia
A biophysical model describing long-range cell-to-cell communication by a diffusible signal mediated by autocrine loops in developing epithelia in the presence of a morphogenetic pre-pattern is introduced. Under a number of approximations, the model reduces to a particular kind of bistable reaction-diffusion equation with strong heterogeneity. In the case of the heterogeneity in the form of a long strip a detailed analysis of signal propagation is...
Weak solutions for anisotropic nonlinear elliptic equations with variable exponents.
Weak solutions for some reaction-diffusion systems with balance law and critical growth with respect to the gradient
Weak solutions of quasilinear elliptic PDE's at resonance
Wiener criterion for degenerate elliptic obstacle problem
We give a Wiener criterion for the continuity of an obstacle problem relative to an elliptic degenerate problem with a weight in the class.
Zum Marx-Shiffmanschen Variationsproblem.
-convergence of concentration problems
In this paper, we use -convergence techniques to study the following variational problemwhere , with , and is a bounded domain of , . We obtain a -convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem . Finally, a second order expansion in -convergence permits to identify the concentration points of the maximizing sequences, also in some non-homogeneous case.
Возмущения квазилинейных эллиптических уравнений и фредгольмовы многообразия
О сильных решениях обобщенной задачи Синьорини.
О сходимости старших производных в проекционных методах
Обобщенное решение задачи типа Дирихле для некоторых сингулярных эллиптических уравнений.