Determining coefficients for a fractional $p$-Laplace equation from exterior measurements

TL;DR

This paper addresses the inverse problem of recovering coefficients in a fractional p-Laplace equation from exterior measurements, providing explicit reconstruction formulas, uniqueness results, and stability estimates.

Contribution

It introduces an explicit reconstruction formula for coefficients, proves global uniqueness for real-analytic coefficients, and establishes stability estimates in the context of fractional p-Laplace equations.

Findings

Explicit reconstruction formula for coefficients

Global uniqueness for real-analytic coefficients

Stability estimate for coefficient determination

Abstract

We consider an inverse problem of determining the coefficients of a fractional $p\,$-Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficents. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set.