On the Resolution of an Inverse Problem by Shape Optimization Techniques

In this work, we want to detect the shape and the location of an inclusion via some boundary measurement on . In practice, the body is immersed in a fluid flowing in a greater domain and governed by the Stokes equations. We study the inverse problem of reconstructing using shape optimization methods by defining the Kohn-Vogelius cost functional. We aim to study the inverse problem with Neumann and mixed boundary conditions.