Stability of Coupled-Physics Inverse Problems with internal measurements

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 $σ|\nabla u|^p$, $0 < p \leq 1$, where $u$ is the solution of the elliptic partial differential equation $\nabla\cdot σ\nabla u =0$ on a bounded domain $Ω$ with boundary conditions $u|_{\partial Ω} = f$. We prove stability of the linearization and Hölder conditional stability for the non-linear problem of recovering $σ$ from the internal measurement.

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