In this work we study the existence of solutions for the following class of quasilinear elliptic
equations− div A (| x|)|∇ u| N− 2∇ u= Q (| x|) f (u), in RN, where N≥ 2 and f has critical …

As in the work of Tartar, we develop here some new results on nonlinear interpolation of α-
Hölderian mappings between normed spaces, by studying the action of the mappings on K …

We present a concise point of view on the first and the second Korn's inequality for general
exponent $ p $ and for a class of domains that includes Lipschitz domains. Our argument is …

We consider S^2-valued maps on a domain Ω⊂R^N minimizing a perturbation of the
Dirichlet energy with vertical penalization in Ω and horizontal penalization on ∂Ω. We first …

In the context of Sobolev spaces with variable exponents, Poincaré–Wirtinger inequalities
are possible as soon as Luxemburg norms are considered. On the other hand, modular …

Multiperforated plates exhibit high gradients and a loss of regularity concentrated in a
boundary layer for which a direct numerical simulation becomes very expensive. For elliptic …

We study scattering and evolution aspects of linear internal waves in a two dimensional
channel with subcritical bottom topography. We define the scattering matrix for the stationary …

We develop a unified strategy to obtain the geometric logarithmic Hardy inequality on any
open set M of a stratified group, provided the validity of the Hardy inequality in this setting …

In the context of Sobolev spaces with variable exponents, Poincar\'e--Wirtinger inequalities
are possible as soon as Luxemburg norms are considered. On the other hand, modular …

This paper builds upon the Caffarelli-Kohn-Nirenberg (CKN) weighted interpolation
inequalities, which are fundamental tools in partial differential equations (PDEs) and …