Local data inverse problem for the polyharmonic operator with anisotropic perturbations

TL;DR

This paper addresses an inverse boundary value problem for polyharmonic operators with tensorial perturbations, establishing unique determination of coefficients from partial boundary data under geometric conditions.

Contribution

It introduces a novel approach to recover tensorial coefficients of polyharmonic operators using local boundary measurements with inaccessible boundary parts.

Findings

Unique determination of tensorial coefficients from partial boundary data

Method applicable under specific geometric assumptions

Advances inverse problems for higher-order operators with anisotropic perturbations

Abstract

In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input can be prescribed nor the output can be measured. We prove the unique determination of all the tensorial coefficients of the operator from the knowledge of the Dirichlet and Neumann map on the accessible part of the boundary, under suitable geometric assumptions on the domain.