Differential and Integral Equations

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

Susanna Terracini

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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.

Article information

Source
Differential Integral Equations, Volume 8, Number 8 (1995), 1911-1922.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369056132

Mathematical Reviews number (MathSciNet)
MR1348957

Zentralblatt MATH identifier
0835.35055

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Citation

Terracini, Susanna. Symmetry properties of positive solutions to some elliptic equations with nonlinear boundary conditions. Differential Integral Equations 8 (1995), no. 8, 1911--1922. https://projecteuclid.org/euclid.die/1369056132


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