Uniqueness in Calder\'on Problem with Partial Data for Less Smooth Conductivities

TL;DR

This paper proves the uniqueness of the inverse conductivity problem with partial data for less smooth conductivities in dimensions three and higher, expanding the class of conductivities for which the problem is solvable.

Contribution

It establishes the uniqueness result for the Calderón problem with partial data for conductivities in the $C^{1}igcap H^{3/2, 2}$ class, a less smooth category than previously considered.

Findings

Uniqueness holds for $C^{1}igcap H^{3/2, 2}$ conductivities in dimensions $n \\geq 3$

Partial data suffices for the uniqueness in the inverse conductivity problem

Extends previous results to less smooth conductivities

Abstract

In this paper we study the inverse conductivity problem with partial data. Moreover, we show that, in dimension $n\geq 3$ the uniqueness of the Calder\'{o}n problem holds for the $C^{1}\bigcap H^{3/2, 2}$ conductivities.