Uniqueness in Calderon's problem with Lipschitz conductivities

TL;DR

This paper proves uniqueness in Calderon's inverse conductivity problem for Lipschitz conductivities, including those close to the identity and arbitrary C^1 conductivities, using X^{s,b}-inspired spaces.

Contribution

It introduces a novel approach using X^{s,b}-inspired spaces to establish uniqueness for Lipschitz conductivities in Calderon's problem.

Findings

Uniqueness for conductivities close to the identity

Uniqueness for arbitrary C^1 conductivities

Application of X^{s,b}-inspired spaces in inverse problems

Abstract

We use X^{s,b}-inspired spaces to prove a uniqueness result for Calderon's problem in a Lipschitz domain under the assumption that the conductivity is Lipschitz. For Lipschitz conductivities, we obtain uniqueness for conductivities close to the identity in a suitable sense. We also prove uniqueness for arbitrary C^1 conductivities.