Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions

Abstract

We study symmetry properties of positive solutions to some semilinear elliptic problems with nonlinear Neumann boundary conditions. We give sufficient conditions to have symmetry around the $\e_n$-axis of positive solutions of problems on the half-space. The proofs are based on the moving plane method. Finally some symmetry results are given in the case when the domain is a ball.