A Shape Optimal Control Problem with Changing Sign Data

Giuseppe Buttazzo (1) , Bozhidar Velichkov (2)

1 Dipartimento di Matematica [Pisa]
2 CVGI - Calcul des Variations, Géométrie, Image

In this paper we consider a shape optimization problem in which the data in the cost functional and in the state equation may change sign, and so no monotonicity assumption is satisfied. Nevertheless, we are able to prove that an optimal domain exists. We also deduce some necessary conditions of optimality for the optimal domain. The results are applied to show the existence of an optimal domain in the case where the cost functional is completely identified, while the right-hand side in the state equation is only known up to a probability P in the space L 2 (D).

Mots clés: shape optimization; free boundary; capacitary measures; stochastic optimization

Domaines: Mathématiques [math]

Giuseppe Buttazzo, Bozhidar Velichkov. A Shape Optimal Control Problem with Changing Sign Data. SIAM Journal on Mathematical Analysis, 2018, 50 (3), pp.2608-2627. ⟨10.1137/17M1126564⟩. ⟨hal-01879182⟩