Electron. J. Diff. Eqns., Vol. 2003(2003), No. 108, pp. 1-20.

Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli

Friedemann Brock

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.

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Friedemann Brock
Universidad de Chile, Facultad de Ciencias
Departamento de Matematicas
Santiago de Chile, Casilla 653, Chile
email: fbrock@uchile.cl
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