Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations

TL;DR

This paper investigates the inverse problem for a fractional Laplace equation with nonlinear lower order terms, establishing well-posedness and unique recoverability of the nonlinearities from exterior measurements.

Contribution

It demonstrates the unique determination of nonlinear lower order terms in fractional Laplace equations from exterior data, extending inverse problem theory.

Findings

The direct problem is well-posed.

The inverse problem has a unique solution.

Nonlinearities can be recovered from exterior measurements.

Abstract

We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.