Spatial localization of the error of constitutive law for the identification of defects in elastic bodies

Abstract

The error on constitutive law (ECL) is a cost functional currently used in inverse problems for identifying interior distribution of coefficients of partial differential equations from overspecified boundary conditions. In previous works, different authors have shown that the ECL permits a good spatial localization of the perturbations of the coefficients. The purpose of this paper is to justify this spatial localization property. The result is obtained for the elliptic equations of elasticity using boundary integral representations of the solutions and comparing the linear and the perturbed solution of the problem.