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May/June 2013 On Serrin's symmetry result in nonsmooth domains and its applications
Juraj Földes
Adv. Differential Equations 18(5/6): 523-548 (May/June 2013).

Abstract

The paper investigates overdetermined fully nonlinear problems on nonsmooth domains. Under natural regularity assumptions on solutions it is shown that overdetermined problems on reflectionally symmetric, bounded domains can have positive solutions only if the domain is a ball. These results are extensions of results of Serrin, who proved this statement for smooth solutions on smooth domains. The results for overdetermined problems are applied to a study of Dirichlet problems, specifically to the question when a nonnegative solution is positive or zero everywhere. As a consequence, an extension of symmetry results of Gidas--Ni--Nirenberg to nonnegative solutions is obtained.

Citation

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Juraj Földes. "On Serrin's symmetry result in nonsmooth domains and its applications." Adv. Differential Equations 18 (5/6) 523 - 548, May/June 2013.

Information

Published: May/June 2013
First available in Project Euclid: 14 March 2013

zbMATH: 1272.35018
MathSciNet: MR3086464

Subjects:
Primary: 35B06, 35B09, 35J25, 35J60, 35N25

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 5/6 • May/June 2013
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