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1999 Approximate radial symmetry for overdetermined boundary value problems
Amandine Aftalion, Jérôme Busca, Wolfgang Reichel
Adv. Differential Equations 4(6): 907-932 (1999).

Abstract

In this paper, we study the stability of Serrin's classical symmetry result for overdetermined boundary value problems [13]. We prove that if there exists a positive solution of $\Delta u +f(u) =0$ in $\Omega$ with $u=0$ on $\partial\Omega$ and if $\partial u / \partial \nu$ on $\partial\Omega$ is close to a constant, then the domain $\Omega$ is close to a ball. Additionally, we give an explicit estimate for the distance of the domain to a circumscribed and inscribed ball. The proof relies on the method of moving planes and new quantitative versions of the Hopf Lemma and Serrin's corner Lemma.

Citation

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Amandine Aftalion. Jérôme Busca. Wolfgang Reichel. "Approximate radial symmetry for overdetermined boundary value problems." Adv. Differential Equations 4 (6) 907 - 932, 1999.

Information

Published: 1999
First available in Project Euclid: 15 April 2013

zbMATH: 0951.35046
MathSciNet: MR1729395

Subjects:
Primary: 35J65
Secondary: 35B50

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.4 • No. 6 • 1999
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