Overdetermined problems for fully nonlinear elliptic equations

Luis Silvestre (1) , Boyan Sirakov (2)

1 Department of Mathematics [Chicago]
2 Departamento de Matematica

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.

Domaines: Equations aux dérivées partielles [math.AP]

Luis Silvestre, Boyan Sirakov. Overdetermined problems for fully nonlinear elliptic equations. 2014. ⟨hal-00851720v2⟩