In this paper, we want to reconstruct the inclusion w via some boundary measurement on ¶W. In practice, the body w is immersed in a fluid flowing in a greater domain W and governed by the Stokes equations. We study the inverse problem of reconstructing w thanks to the tools of shape optimization by defining the Kohn-Vogelius cost function. We prove the existence of the first order shape derivative of the cost function.

inverse problem, shape optimization, Kohn-Vogelius cost function.