The fractional Calder\'on problem

TL;DR

This paper reviews recent advances in the fractional Calderón problem, focusing on determining unknown coefficients in fractional Schrödinger equations from exterior measurements, highlighting its unique properties and implications for inverse problems.

Contribution

It provides a comprehensive overview of recent progress, emphasizing the equation's uniqueness and approximation capabilities that enhance inverse problem solutions.

Findings

Unique determination of coefficients from exterior data

Strong approximation properties of fractional Schrödinger equations

Implications for solving related inverse problems

Abstract

We review recent progress in the fractional Calder\'on problem, where one tries to determine an unknown coefficient in a fractional Schr\"odinger equation from exterior measurements of solutions. This equation enjoys remarkable uniqueness and approximation properties, which turn out to yield strong results in related inverse problems.