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Symmetry in multi-phase overdetermined problems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
Dept. of Mathematics, Faculty of Science and Letters, Istanbul Technical University.
2011 (English)In: Journal of Convex Analysis, ISSN 0944-6532, Vol. 18, 1013-1024 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Symmetry, overdetermined problems, multi-phases, viscosity solu- tions, Green’s function.
National Category
URN: urn:nbn:se:kth:diva-82098ISI: 000304571400006ScopusID: 2-s2.0-84855797557OAI: diva2:497936

QC 20120213

Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2013-04-29Bibliographically approved

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