On symmetry results for elliptic equations with convex nonlinearities

TL;DR

This paper studies the partial symmetry of solutions to elliptic equations with convex nonlinearities in symmetric domains, providing insights into the symmetry properties of such solutions.

Contribution

It offers new results on symmetry properties of solutions to elliptic equations with convex nonlinearities in symmetric domains.

Findings

Solutions exhibit partial symmetry in axially or radially symmetric domains.

Convex nonlinearities influence the symmetry behavior of solutions.

The results extend existing symmetry results to broader classes of elliptic problems.

Abstract

We investigate partial symmetry of solutions to semi-linear and quasi-linear elliptic problems with convex nonlinearities, in domains that are either axially symmetric or radially symmetric.