Valeurs propres de systèmes elliptiques définis sur des sous espaces
Vanishing non-local regularization of a scalar conservation law.
Vanishing of solutions of diffusion equation with convection and absorption.
Vanishing viscosity limit for an expanding domain in space
Vanishing waves on closed intervals and propagating short-range phenomena.
Variable depth KdV equations and generalizations to more nonlinear regimes
We study here the water waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known that, for such regimes, a generalization of the KdV equation (somehow linked to the Camassa-Holm equation) can be derived and justified [Constantin and Lannes, Arch. Ration. Mech. Anal. 192 (2009) 165–186] when the bottom is flat. We generalize here this result with a new class of equations taking into account...
Variance decay for functionals of the environment viewed by the particle
For the random walk among random conductances, we prove that the environment viewed by the particle converges to equilibrium polynomially fast in the variance sense, our main hypothesis being that the conductances are bounded away from zero. The basis of our method is the establishment of a Nash inequality, followed either by a comparison with the simple random walk or by a more direct analysis based on a martingale decomposition. As an example of application, we show that under certain conditions,...
Variants on Alexandrov reflection principle and other applications of maximum principle
Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket
Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.
Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces.
Variational characterization of interior interfaces in phase transition models on convex plane domains.
Variational inequalities and rearrangements
We give comparison results for solutions of variational inequalities, related to general elliptic second order operators, involving solutions of symmetrized problems, using Schwarz spherical symmetrization.
Variational inequalities for vector-valued functions.
Variational methods in nonlinear problems
Various kinds of sensitive singular perturbations
We consider variational problems of P. D. E. depending on a small parameter when the limit process implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...
Varying domains in a general class of sublinear elliptic problems.
Verallgemeinerungen eines Satzes von Leighton über die Oszillation selbstadjungierter Differentialgleichungen
Vibrations de classe Cs 2 des tores plats de dimension s et théorie des nombres.
Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem
Viscosity solutions of elliptic partial differential equations.