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arXiv · 1306.6673

Overdetermined problems for fully nonlinear elliptic equations

Luis Silvestre·Boyan Sirakov
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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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Luis Silvestre, Boyan Sirakov. 2013-06-27. Overdetermined problems for fully nonlinear elliptic equations. https://arxiv.org/abs/1306.6673

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