Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions. (English) Zbl 0835.35055

Author’s 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 \({\mathbf e}_n\)-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.
Reviewer: M.Biroli (Monza)


35J65 Nonlinear boundary value problems for linear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs