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

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.