Stability of Coupled-Physics Inverse Problems with internal measurements

Abstract

In this paper, we develop a general approach to prove stability for the non linear second step of hybrid inverse problems. We work with general functionals of the form $\sigma |\nabla u{|}^p$, $0<p\le 1$, where $u$ is the solution of the elliptic partial differential equation $\nabla \cdot \sigma \nabla u=0$ on a bounded domain $\Omega$ with boundary conditions $u{|}_{\partial \Omega }=f$. We prove stability of the linearization and Hölder conditional stability for the non-linear problem of recovering $\sigma$ from the internal measurement.