Symmetry for solutions of two-phase semilinear elliptic equations on hyperbolic space

Simple item page
dc.creatorBirindelli, Isabeau
dc.creatorMazzeo, Rafe
dc.date2008-06-18
dc.date.accessioned2026-07-07T09:45:19Z
dc.date.available2026-07-07T09:45:19Z
dc.descriptionAssume that $f(s) = F'(s)$ where $F$ is a double-well potential. Under certain conditions on the Lipschitz constant of $f$ on $[-1,1]$, we prove that arbitrary bounded global solutions of the semilinear equation $Δu = f(u)$ on hyperbolic space $\HH^n$ must reduce to functions of one variable provided they admit asymptotic boundary values on the infinite boundary of $\HH^n$ which are invariant under a cohomogeneity one subgroup of the group of isometries of $\HH^n$. We also prove existence of these one-dimensional solutions.
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/0806.2952
dc.identifierhttp://arxiv.org/abs/0806.2952
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/163158
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.subject35J60; 58J05
dc.titleSymmetry for solutions of two-phase semilinear elliptic equations on hyperbolic space
dc.typetext

Files

Collections

arXiv