Stability of the Calder\'on problem for less regular conductivities

TL;DR

This paper establishes log-type stability estimates for the Calderón problem when conductivities are in the class C^{1,ε}, extending previous uniqueness results to include stability analysis for less regular conductivities.

Contribution

It provides the first stability results for the Calderón problem with conductivities in C^{1,ε}, broadening the class of conductivities for which stability can be achieved.

Findings

Proves log-type stability for conductivities in C^{1,ε}

Extends stability results beyond previous uniqueness theorems

Builds on methods from Haberman and Tataru's work

Abstract

In these notes we prove log-type stability for the Calder\'on problem with conductivities in $ C^{1,\varepsilon}(\bar{\Omega}) $. We follow the lines of a recent work by Haberman and Tataru in which they prove uniqueness for $ C^1(\bar{\Omega}) $.