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Overdetermined problems for fully nonlinear elliptic equations (1306.6673v1)
Published 27 Jun 2013 in math.AP
Abstract: We prove that the existence of a solution to a fully nonlinear elliptic equation in a bounded domain $\Omega$ with an overdetermined boundary condition prescribing both Dirichlet and Neumann constant data forces the domain $\Omega$ to be a ball. This is a generalization of Serrin's classical result from 1971.
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