Radial symmetry of minimax critical points for nonsmooth functionals

TL;DR

This paper proves the existence of radially symmetric, decreasing solutions for a broad class of quasi-linear elliptic problems using a novel nonsmooth symmetric minimax principle.

Contribution

It introduces a nonsmooth version of a symmetric minimax principle to establish radial symmetry in solutions of elliptic problems.

Findings

Existence of radially symmetric solutions for quasi-linear elliptic problems.

Application of nonsmooth minimax principle to symmetry results.

Extension of symmetric minimax methods to nonsmooth settings.

Abstract

We obtain the existence of radially symmetric and decreasing solutions to a general class of quasi-linear elliptic problems by a nonsmooth version of a symmetric minimax principle recently obtained by Jean Van Schaftingen.