Symmetry in multi-phase overdetermined problems
2011 (English)In: Journal of Convex Analysis, ISSN 0944-6532, Vol. 18, 1013-1024 p.Article in journal (Refereed) Published
In this paper we prove symmetry for a multi-phase overdetermined problem, with nonlinear governing equations. The most simple form of our problem (in the two-phase case) is as follows: For a bounded C-1 domain Omega subset of R-n (n >= 2) let u(+) be the Green's function (for the p-Laplace operator) with pole at some interior point (origin, say), and u(-) the Green's function in the exterior with pole at infinity. If for some strictly increasing function F(t) (with some growth assumption) the condition partial derivative(v)u(+) = F(partial derivative(v)u(-)) holds on the boundary partial derivative Omega, then Omega is necessarily a ball. We prove the more general multi-phase analog of this problem.
Place, publisher, year, edition, pages
2011. Vol. 18, 1013-1024 p.
Symmetry, overdetermined problems, multi-phases, viscosity solu- tions, Green’s function.
IdentifiersURN: urn:nbn:se:kth:diva-82098ISI: 000304571400006ScopusID: 2-s2.0-84855797557OAI: oai:DiVA.org:kth-82098DiVA: diva2:497936
QC 201202132012-02-112012-02-112013-04-29Bibliographically approved