Symmetry and monotonicity of solutions to some variational problems in cylinders and annuli
Date
2003-10-24
Authors
Brock, Friedemann
Journal Title
Journal ISSN
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. <i>Electronic Journal of Differential Equations, 2003</i>(108), pp. 1-20.
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Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.