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

TLDR: In this article, the inverse boundary value problem of determining the potential q = 0 in the reduced wave equation was considered and a result of global Lipschitz stability was obtained in dimension n/geq 3 for potentials that are piecewise linear on a given partition of Euclidean space.

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 $n\\geq 3$ 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 $\\Delta u + k^2c^{-2}u=0$ at fixed frequency $k$.