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

Date

2003-10-24

Authors

Brock, Friedemann

Journal Title

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Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

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 (-α, α) x ω, where ω is a bounded smooth domain in ℝN-1. The admissible functions satisfy periodic boundary conditions on {±α} x ω, 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.

Description

Keywords

Variational problems, Periodic boundary conditions, Neumann problem, Symmetry of solutions, Elliptic equation, Cylinder, Annulus

Citation

Brock, F. (2003). Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli. Electronic Journal of Differential Equations, 2003(108), pp. 1-20.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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