Optimal stability in the identification of a rigid inclusion in an isotropic Kirchhoff-Love plate

TL;DR

This paper addresses the inverse problem of identifying a rigid inclusion within an elastic isotropic Kirchhoff-Love plate using boundary measurements, providing a stability estimate based on advanced mathematical inequalities.

Contribution

It introduces a constructive stability estimate of log type for the inverse problem, utilizing a novel boundary three spheres inequality for the plate's equation.

Findings

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

Applied a boundary three spheres inequality to improve stability analysis.

Provided a mathematical framework for detecting inclusions in elastic plates.

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 and isotropic material. Under suitable a priori regularity assumptions on the boundary of the inclusion, we prove a constructive stability estimate of log type. Key mathematical tool is a recently proved optimal three spheres inequality at the boundary for solutions to the Kirchhoff-Love plate's equation.