Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 108, pp. 1-20.
Title: Symmetry and monotonicity of solutions to some variational
problems in cylinders and annuli
Author: Friedemann Brock (Univ. de Chile, Santiago de Chile)
Abstract:
We prove symmetry and monotonicity properties for local minimizers
and stationary solutions of some variational problems
related to semilinear elliptic equations in a cylinder
$(-a,a)\times \omega$, where $\omega $
is a bounded smooth domain in $\mathbb{R}^{N-1}$.
The admissible functions satisfy periodic boundary conditions on
$\{\pm a\} \times \omega $, and some other conditions.
We show also symmetry properties for related problems
in annular domains. Our proofs are based on rearrangement arguments
and on the Moving Plane Method.
Submitted March 9, 2003. Published October 24, 2003.
Math Subject Classifications: 35J25, 35B10, 35B35, 35B50, 35J20.
Key Words: Variational problem; periodic boundary conditions;
Neumann problem; symmetry of solutions; elliptic equation;
cylinder; annulus.