Boundary integral formulae for the reconstruction of imperfections of small diameter in an elastic medium

We consider an isotropic Lame system for an elastic medium consisting of fi nitely many imperfections of small diameter, embedded in a homogeneous refe rence 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, th e location of the imperfections, and their geometry. Second, we use this as ymptotic 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 identifica tion procedure.