Nonlinear Elliptic Equations Involving Critical Sobolev Exponents: Asymptotic Analysis via Methods of Epi-Convergence

Abstract

We study the minimizers of two functionals involving critical Sobolev exponents, and whose Euler equations lead to nonlinear boundary value problems. We first employ classical methods to obtain estimates. We then rephrase the problems in a more abstract functional analytical setting. We use epi-convergence arguments in order to describe the behaviour of the minimizers.