Stability estimates for the inverse boundary value problem by partial Cauchy data

TL;DR

This paper establishes stability estimates for the inverse conductivity problem with partial boundary data in dimensions three and higher, assuming the conductivity has specific regularity properties.

Contribution

It provides new stability estimates for the inverse boundary value problem under partial data and regularity conditions on the conductivity.

Findings

Derived stability estimates for the inverse problem.

Applicable to conductivities with $C^{1,\sigma}$ and $H^{3/2+\sigma}$ regularity.

Extends understanding of inverse problems with partial boundary data.

Abstract

In this paper we study the inverse conductivity problem with partial data in dimension $n\geq 3$. We derive stability estimates for this inverse problem if the conductivity has $C^{1,\sigma}(\bar\Omega)\cap H^{3/2+\sigma}(\Omega)$ regularity for $0<\sigma<1$.