Recovery of the Derivative of the Conductivity at the Boundary

TL;DR

This paper presents a method to reconstruct both the conductivity and its normal derivative at the boundary from boundary measurements, establishing uniqueness of the conductivity in the bulk for certain regularity classes in higher dimensions.

Contribution

It introduces a boundary reconstruction technique for conductivity and its derivative, proving uniqueness results in higher-dimensional inverse boundary value problems.

Findings

Reconstruction of conductivity and its normal derivative at the boundary.

Uniqueness of conductivity in the bulk for specific Sobolev regularity classes.

Applicable in dimensions n ≥ 5 with p ≥ n.

Abstract

We describe a method to reconstruct the conductivity and its normal derivative at the boundary from the knowledge of the potential and current measured at the boundary. This boundary determination implies the uniqueness of the conductivity in the bulk when it lies in $W^{1+\frac{n-5}{2p}+,p}$, for dimensions $n\ge 5$ and for $n\le p<\infty$.