A symmetry problem for a singular equation

ANEDDA, CLAUDIA

2004-01-01

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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.