The Steklov Spectrum on Moving Domains

详细信息    查看全文

• 作者：Beniamin Bogosel
• 关键词：Eigenvalues ; Steklov spectrum ; Shape optimization
• 刊名：Applied Mathematics & Optimization
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：75
• 期：1
• 页码：1-25
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Phy
• 出版者：Springer US
• ISSN：1432-0606
• 卷排序：75

文摘

We study the continuity of the Steklov spectrum on variable domains with respect to the Hausdorff convergence. A key point of the article is understanding the behaviour of the traces of Sobolev functions on moving boundaries of sets satisfying an uniform geometric condition. As a consequence, we are able to prove existence results for shape optimization problems regarding the Steklov spectrum in the family of sets satisfying a \(\varepsilon \)-cone condition and in the family of convex sets.