Shape optimization method for an inverse geometric source problem and stability at critical shape

<p style='text-indent:20px;'>This work deals with a geometric inverse source problem. It consists in recovering inclusion fixed domain based on boundary measurements. The problem is solved via shape optimization formulation. Two cost functions are investigated, namely, the least squares fitting, and Kohn-Vogelius function. In this case, existence of derivative given first order material state problems. Furthermore, using adjoint approach, gradient both characterized. Then, stability investigated by proving compactness Hessian at critical for considered cases. Finally, method, steepest descent algorithm developed, some numerical experiments non-parametric shapes discussed.</p>