Worst-case shape optimization for the Dirichlet energy. (April 2017)

• Record Type: Journal Article
• Authors: Bellido, José Carlos; Buttazzo, Giuseppe; Velichkov, Bozhidar
• Is Part Of: Nonlinear analysis. Volume 153(2017)
• Page Start: 117
• Page End: 129
• Publication Date: 2017-04
• Subjects: 49J45 -- 49R05 -- 35P15 -- 47A75 -- 35J25; Shape optimization -- Dirichlet energy -- Worst-case optimization; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.05.014
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the optimization problem for a shape cost functional F ( Ω, f ) which depends on a domain Ω varying in a suitable admissible class and on a "right-hand side" f . More precisely, the cost functional F is given by an integral which involves the solution u of an elliptic PDE in Ω with right-hand side f ; the boundary conditions considered are of the Dirichlet type. When the function f is only known up to some degree of uncertainty, our goal is to obtain the existence of an optimal shape in the worst possible situation. Some numerical simulations are provided, showing the difference in the optimal shape between the case when f is perfectly known and the case when only the worst situation is optimized.