Shape sensitivity analysis for a Robin problem via minimax differentiability

This paper deals with shape sensitivity analysis for a Robin problem. The structure of Eulerian derivative with respect to the shape of the variable domain for a cost functional is established by using differentiability of a minimax combing with function space parametrization and function space embedding. Finally we apply a gradient type algorithm to our problem. Numerical examples show that our theory is very useful for practical purpose and the algorithm is feasible.