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SYMMETRY RESULT FOR SOME OVERDETERMINED VALUE PROBLEMS

Part of: Partial differential equations Elliptic equations and systems

Published online by Cambridge University Press:  01 April 2008

MOHAMMED BARKATOU  and
SAMIRA KHATMI
MOHAMMED BARKATOU*
Affiliation:
Department of Mathematics and Informatics, University of Chouaïb Doukkali, El Jadida, Morocco (email: [email protected])
SAMIRA KHATMI
Affiliation:
University Laval, Québec, Canada
*
✉For correspondence; e-mail: [email protected]
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Abstract

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The aim of this article is to prove a symmetry result for several overdetermined boundary value problems. For the two first problems, our method combines the maximum principle with the monotonicity of the mean curvature. For the others, we use essentially the compatibility condition of the Neumann problem.

Keywords

compatibility conditionmean curvatureNeumann problemoverdetermined problemSerrin problemshape optimizationsymmetry

MSC classification

Secondary: 35A15: Variational methods 35J65: Nonlinear boundary value problems for linear elliptic equations 35B50: Maximum principles
Type
Research Article
Information
The ANZIAM Journal , Volume 49 , Issue 4 , April 2008 , pp. 479 - 494
Copyright
Copyright © Australian Mathematical Society 2008

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