Symmetry results for nonvariational quasi-linear elliptic systems

TL;DR

This paper establishes symmetry properties of solutions to certain non-variational quasi-linear elliptic systems, demonstrating axial and radial symmetry in specific domains, and analyzing the two-dimensional case in a half-space.

Contribution

It introduces a weak comparison principle to prove symmetry results for non-variational elliptic systems, extending known symmetry techniques to new classes of problems.

Findings

Axial symmetry in convex, symmetric domains

Radial symmetry in balls for regular solutions

Analysis of the two-dimensional half-space case

Abstract

By virtue of a weak comparison principle in small domains we prove axial symmetry in convex and symmetric smooth bounded domains as well as radial symmetry in balls for regular solutions of a class of quasi-linear elliptic systems in non-variational form. Moreover, in the two dimensional case, we study the system when set in a half-space.