Optimal stability estimate of the inverse boundary value problem by partial measurements

TL;DR

This paper establishes improved log-type stability estimates for inverse boundary value problems with partial measurements, enhancing previous results that had log-log estimates, thus advancing the understanding of inverse potential and conductivity problems.

Contribution

The work provides sharper log-type stability estimates for inverse problems with partial data, improving upon earlier log-log estimates and broadening the theoretical understanding.

Findings

Established log-type stability estimates for inverse potential and conductivity problems.

Improved stability estimates from log-log to log-type with partial data.

Enhanced theoretical framework for inverse boundary value problems with inaccessible boundary parts.

Abstract

In this work we establish log-type stability estimates for the inverse potential and conductivity problems with partial Dirichlet-to-Neumann map, where the Dirichlet data is homogeneous on the inaccessible part. This result, to some extent, improves our former result on the partial data problem in which log-log-type estimates were derived.