Boundary determination of the Lam\'e moduli for the isotropic elasticity system

TL;DR

This paper develops explicit formulas to determine the Lamé moduli and their derivatives at the boundary of an isotropic elastic medium using localized boundary measurements, advancing inverse boundary value problem solutions.

Contribution

It provides the first explicit pointwise reconstruction formulas for Lamé moduli and their derivatives at the boundary under minimal regularity assumptions.

Findings

Explicit boundary reconstruction formulas derived

Reconstruction of Lamé moduli and derivatives achieved

Applicable under minimal regularity assumptions

Abstract

We consider the inverse boundary value problem of determining the Lam\'e moduli of an isotropic, static elasticity equations of system at the boundary from the localized Dirichlet-to-Neumann map. Assuming appropriate local regularity assumptions as weak as possible on the Lam\'e moduli and on the boundary, we give explicit pointwise reconstruction formulae of the Lam\'e moduli and their higher order derivatives at the boundary from the localized Dirichlet-to-Neumann map.