Sym\'etrie des grandes solutions d'\'equations elliptiques semi lin\'eaire

TL;DR

This paper proves that solutions to certain semi-linear elliptic equations in a ball are radially symmetric if they tend to infinity at the boundary, under conditions on the nonlinearity.

Contribution

It establishes symmetry of solutions for a class of semi-linear elliptic equations with asymptotically convex nonlinearities.

Findings

Solutions are radially symmetric under given conditions.

Symmetry holds for solutions tending to infinity at the boundary.

Results apply to equations with asymptotically convex nonlinearities.

Abstract

We prove that, if $g$ is a continuous asymptotically convex function, any solution $u$ of $-\Delta u+g(u)=0$ in a ball B which tends to infinity on $\partial B$ is radially symmetric.