Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data

Abstract

We consider the inverse boundary value problem of determining the potential $q$ in the equation $\Delta u+qu=0$ in $\Omega \subset {\mathbb{R}}^n$, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension $n\ge 3$ for potentials that are piecewise linear on a given partition of $\Omega$. No sign, nor spectrum condition on $q$ is assumed, hence our treatment encompasses the reduced wave equation $\Delta u+k^2{c}^{-2}u=0$ at fixed frequency $k$.

36 pages, submitted