The inverse problem for the fractional conductivity equation: a survey

TL;DR

This survey reviews recent advances in the inverse problem for fractional conductivity equations, focusing on determining unknown coefficients from exterior measurements in nonlocal elliptic equations.

Contribution

It compiles and discusses recent results specifically related to the conductivity formulation of the fractional Calderón problem, highlighting progress in this area.

Findings

Recent results on the fractional Calderón problem are summarized.

The survey emphasizes developments in the conductivity formulation.

Key techniques and open questions are discussed.

Abstract

The fractional Calder\'on problem asks to determine the unknown coefficients in a nonlocal, elliptic equation of fractional order from exterior measurements of its solutions. There has been substantial work on many aspects of this inverse problem. In this review we collect some recent results related to the conductivity formulation of the fractional Calder\'on problem.