Overdetermined problems for fully nonlinear elliptic equations

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.

19 pages

References in corpus (1)

• Singular solutions of fully nonlinear elliptic equations and applications

Cited by in corpus (1)

• Symmetry of minimizers with a level surface parallel to the boundary