We discuss an overdetermined problem associated with a particular singular elliptic equation in a bounded domain \Omega \subset R^N. We prove that if the solution u vanishes and if the gradient |\Nabla u| is a constant on the boundary \partial \Omega then \Omega must be a ball, extending a well known result for regular equations.

A symmetry problem for a singular equation

ANEDDA, CLAUDIA
2004-01-01

Abstract

We discuss an overdetermined problem associated with a particular singular elliptic equation in a bounded domain \Omega \subset R^N. We prove that if the solution u vanishes and if the gradient |\Nabla u| is a constant on the boundary \partial \Omega then \Omega must be a ball, extending a well known result for regular equations.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/94408
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