Partial data stability for the inverse fractional conductivity problem

TL;DR

This paper investigates the stability of an inverse fractional conductivity problem with partial data, establishing log-log and sharper logarithmic stability estimates under specific conditions.

Contribution

It introduces new stability estimates for the inverse fractional conductivity problem with partial data, extending understanding beyond classical Calderón problem results.

Findings

Log-log stability estimate when conductivities agree in measurement set

Sharper logarithmic stability when conductivities agree outside the domain

Advances in partial data inverse problems for fractional operators

Abstract

The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity problem on bounded smooth domains. Using the fractional Liouville reduction, we obtain a log-log stability estimate when the conductivities a priori agree in the measurement set and their difference has compact support. In the case in which the conductivities are assumed to agree a priori in the whole exterior of the domain, we obtain a shaper logarithmic stability estimate.