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 $L^2(D)$.

A shape optimal control problem with changing sign data

Giuseppe Buttazzo
;
Bozhidar Velichkov
2018-01-01

Abstract

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 $L^2(D)$.
2018
Buttazzo, Giuseppe; Velichkov, Bozhidar
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/939299
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