Brock, Friedemann2021-01-272021-01-272003-10-24Brock, 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. 1-20.1072-6691https://hdl.handle.net/10877/13159We 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.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalVariational problemsPeriodic boundary conditionsNeumann problemSymmetry of solutionsElliptic equationCylinderAnnulusArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.