Symmetry of large solutions of nonlinear elliptic equations in a ball

TL;DR

This paper proves that large solutions of certain nonlinear elliptic equations in a ball are necessarily radially symmetric, under conditions on the nonlinearity g.

Contribution

It establishes the symmetry of large solutions for a class of nonlinear elliptic equations with specific conditions on g, extending previous symmetry results.

Findings

Large solutions are radially symmetric in a ball.

Symmetry holds under Keller-Osserman and convexity at infinity conditions.

Results apply to a broad class of nonlinearities g.

Abstract

Let $g$ be a locally Lipschitz continuous real valued function which satisfies the Keller-Osserman condition and is convex at infinity, then any large solution of $-\Delta u+g(u)=0$ in a ball is radially symmetric.