Stable determination of a rigid inclusion in an anisotropic elastic plate

TL;DR

This paper addresses the challenging inverse problem of identifying a rigid inclusion within an anisotropic elastic plate using boundary measurements, providing a stability estimate despite the problem's severe ill-posedness.

Contribution

It introduces a stability estimate of log-log type for determining rigid inclusions in anisotropic plates, advancing understanding of inverse problems in elastic media.

Findings

Established a log-log stability estimate for the inverse problem.

Proved stability under regularity assumptions on the inclusion boundary.

Extended results to non-homogeneous anisotropic materials.

Abstract

In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of the plate. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. For this severely ill-posed problem, under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a stability estimate of log-log type.