Domain Identification for a Nonlinear Elliptic Equation

Abstract

It is proposed to identify the domain $\Omega \in {\mathbb{R}}^n$ of a nonlinear elliptic equation subject to given Cauchy data on part of the known outer boundary $\Gamma$ and to the zero condition on the unknown inner boundary $\gamma$. It is proved that under the assumption $\dot{\bar{\Omega }}=\Omega$, the domain $\Omega$ is uniquely determined.