Global uniqueness for the Calder\'on problem with Lipschitz conductivities

TL;DR

This paper proves the uniqueness of solutions for Calderón's inverse conductivity problem with Lipschitz conductivities in higher dimensions, confirming a longstanding conjecture and extending previous results to more general conductivities.

Contribution

It establishes the first global uniqueness result for Lipschitz conductivities in higher dimensions, building on and extending prior work for smoother conductivities.

Findings

Uniqueness for Lipschitz conductivities in higher dimensions

Confirms Uhlmann's conjecture

Extends prior results to more general conductivities

Abstract

We prove uniqueness for Calder\'on's problem with Lipschitz conductivities in higher dimensions. Combined with the recent work of Haberman, who treated the three and four dimensional cases, this confirms a conjecture of Uhlmann. Our proof builds on the work of Sylvester and Uhlmann, Brown, and Haberman and Tataru who proved uniqueness for $C^1$ conductivities and Lipschitz conductivities sufficiently close to the identity.