Overdetermined problems for fully nonlinear elliptic equations

2013/06/27 by Silvestre, Luis, Sirakov, Boyan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.6673

Abstract

We prove that the existence of a solution to a fully nonlinear elliptic equation in a bounded domain Ω with an overdetermined boundary condition prescribing both Dirichlet and Neumann constant data forces the domain Ω to be a ball. This is a generalization of Serrin's classical result from 1971.

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