Calculus of Variations and Geometric Measure Theory

G. Buttazzo - B. Velichkov

A shape optimal control problem and its probabilistic counterpart

created by buttazzo on 21 Apr 2017
modified by velichkov on 21 Apr 2018


Accepted Paper

Inserted: 21 apr 2017
Last Updated: 21 apr 2018

Journal: SIAM J. Math. Anal.
Pages: 16
Year: 2017


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 $L^2(D)$.

Keywords: shape optimization, capacitary measures, free boundary, stochastic optimization