# Stable determination of a Lam\'e coefficient by one internal measurement of displacement

## TL;DR

This paper demonstrates that the shear modulus of an elastic body can be stably determined from a single internal displacement measurement, with boundary data independent of the unknown elasticity tensor.

## Contribution

It introduces a method to recover the shear modulus using only one internal measurement, enhancing stability and reducing data requirements compared to previous approaches.

## Key findings

- Stable recovery of shear modulus from one internal measurement
- Boundary data can be assigned independently of the elasticity tensor
- Method applicable to isotropic elastic bodies

## Abstract

In this paper we show that the shear modulus $\mu$ of an isotropic elastic body can be stably recovered by the knowledge of one single displacement field whose boundary data can be assigned independently of the unknown elasticity tensor.