Identification of the shape of the inclusion in the anisotropic elastic body

Abstract

Consider an elastic body which occupies a domain Let D denote an open subset with Lipschitz boundary compactly contained in Ω. Suppose the elasticity tensor field of Ω has the form where C_o is a homogeneous anisotropic elasticity tensor field. Denote by the traction on ∂Ω corresponding to a displacement field f on ∂Ω. We assume that (i) is connected; (ii) all component of H are just essentially bounded in D; (iii) H satisfies a jump condition in a relative neighbourhood of ∂D in D

Under this assumption, we prove the unique determination of D by means of for infinitely many f. The proof is due to making use of a system of integral inequalities, the Runge approximation theorem and singular solutions.

Keywords:

• Dirichlet—to—Neumann map
• elasticity tensor
• identification of inclusion
• inverse boundary value problem
• anisotropic