Boundary Integral Formulae for the Reconstruction of Imperfections of Small Diameter in an Elastic Medium

Abstract

We consider an isotropic Lame system for an elastic medium consisting of finitely many imperfections of small diameter, embedded in a homogeneous reference medium. The Lame coefficients of the imperfections are different from those of the background medium. First, we establish an asymptotic formula for the displacement vector in terms of the reference Lame coefficients, the location of the imperfections, and their geometry. Second, we use this asymptotic expansion to establish continuous dependence estimates for certain characteristics of the imperfections in terms of the boundary data and to derive integral boundary formulae that yield to a very effective identification procedure.