 
Summary: Boundary Integral Formulae for the Reconstruction of
Imperfections of Small Diameter in an Elastic Medium
Carlos Alves y and Habib Ammari z
Abstract
We consider an isotropic Lame system for an elastic medium consisting of nitely
many imperfections of small diameter, embedded in a homogeneous reference medium.
The Lame coeÆcients of the imperfections are dierent from those of the background
medium. Firstly we establish an asymptotic formula for the displacement vector in
terms of the reference Lame coeÆcients, the location of the imperfections and their ge
ometry. Secondly 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 eective identication
procedure.
Key words. Inverse elastic problem, Lame equation, elastic imperfections, recon
struction
1991 AMS subject classications. 73D50, 35R30, 35B30
1 Introduction
The non destructive inspection technique has recently received considerable attention in
the applied mathematical, as well as in the engineering, literature. Using this technique
one seeks to determine information about elastic parameters of an elastic medium based
