Integral stability of Calder\'on inverse conductivity problem in the plane

TL;DR

This paper proves that in two-dimensional Lipschitz domains, the Calderón inverse conductivity problem exhibits stability in the $L^p$ sense when conductivities are bounded in fractional Sobolev spaces, advancing understanding of inverse problems.

Contribution

It establishes $L^p$ stability for the Calderón problem in 2D with conductivities in fractional Sobolev spaces, a novel result in inverse conductivity analysis.

Findings

Stability in the $L^p$ sense for the inverse problem.

Applicability to conductivities in fractional Sobolev spaces.

Extension of stability results to Lipschitz domains.

Abstract

It is proved that, in two dimensions, the Calder\'on inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0, 1<p<\infty$.