Uniqueness in the Calderón problem via infinitesimally bounded potentials

Abstract

The Calderón problem is an inverse problem with applications to electrical impedance tomography and geophysical prospection. We prove uniqueness in the Calderón problem in spatial dimension $n\ge 3$ for scalar conductivities in the Sobolev space $W^{1,p}$ with $p\ge n$. This generalizes a result of Haberman who considered the case $p\ge n$ and $n=3$ or $4$. Our method of proof combines a Fourier series approach with an analytic criterion for infinitesimal boundedness of potentials appearing in a Schrödinger equation with respect to the Laplacian.

This paper has been withdrawn due to errors in the crucial estimates in Lemma 1 and Theorem 5