An Inverse Problem on Determining Second Order Symmetric Tensor for Perturbed Biharmonic Operator

TL;DR

This paper investigates an inverse problem for a perturbed biharmonic operator, demonstrating that second order symmetric tensor, first order vector, and potential can be uniquely identified from boundary measurements.

Contribution

It establishes the unique determination of second order symmetric tensor, first order vector, and potential in a higher order elliptic operator from boundary data.

Findings

Unique recovery of second order symmetric tensor

Determination of first order vector field

Identification of zero-th order potential

Abstract

This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.