Lipschitz Stability for Polyhedral Elastic Inclusions from Partial Data

TL;DR

This paper establishes a Lipschitz stability estimate for identifying polyhedral elastic inclusions within a homogeneous isotropic elastic body using partial boundary measurements, advancing inverse problem solutions.

Contribution

It provides a constructive Lipschitz stability estimate for the inverse problem of determining polyhedral inclusions from partial boundary data.

Findings

Lipschitz stability estimate proven for the inverse problem

Constructive method developed for boundary data analysis

Applicable to polyhedral inclusions in elastic bodies

Abstract

The paper deals with the inverse problem of determining a polyhedral inclusion compactly contained in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and the body are made of homogeneous isotropic material. Under suitable assumptions on the geometry of the unknown inclusion, we prove a constructive Lipschitz stability estimate from the local Dirichlet-to-Neumann map.