Sensitivity analysis for some inverse problems in linear elasticity via minimax differentiability

In this article, we consider the inverse problem of recovering a piecewise constant Lamé parameters by a single boundary measurement. We also consider the geometric inverse problem of locating the interface where the jump of the parameters occurs. These problems turn out to an optimization problems by making use of the Kohn–Vogelius cost function. We rewrite the functional in a min–sup form and we use the differentiability of the min–sup combined with the function space parametrization and the function space embedding to get the optimality condition. These techniques allow us to avoid the differentiability of the states variables with respect to the shape or the Lamé parameters. We apply an iterative algorithm and we give some numerical results.