Shape optimization problems with Robin conditions on the free boundary

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• 作者：Dorin Bucur^a ; ¹ ; ^{dorin.bucur@univ-savoie.fr" class="auth_mail" title="E-mail the corresponding author} ; Alessandro Giacomini^b ; ² ; ^{alessandro.giacomini@unibs.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Free boundary problems ; Shape optimization problems ; Robin boundary conditions ; Free discontinuity problems ; Functions of bounded variation
• 刊名：Annales de l'Institut Henri Poincare (C) Non Linear Analysis
• 出版年：2016
• 出版时间：November-December 2016
• 年：2016
• 卷：33
• 期：6
• 页码：1539-1568
• 全文大小：467 K

文摘

We provide a free discontinuity approach to a class of shape optimization problems involving Robin conditions on the free boundary. More precisely, we identify a large family of domains on which such problems are well posed in a way that the extended problem can be considered a relaxed version of the corresponding one on regular domains, we prove existence of a solution and obtain some qualitative information on the optimal sets.