Fractional capacities relative to bounded open Lipschitz sets complemented

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• 作者：S. Shi ; J. Xiao
• 关键词：Mathematics Subject ClassificationPrimary 31B15 ; 31B35 ; Secondary 42B35 ; 42B37 ; 49R05
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：56
• 期：1
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0835
• 卷排序：56

文摘

As a complement of (Shi and Xiao in Potential Anal 45:261–298, 2016) this article addresses five more aspects of the fractional capacities relative to bounded open Lipschitz subsets of \({\mathbb {R}}^n\): (i) quasi-everywhere version; (ii) unique extremal; (iii) energy functional; (iv) dual representation; (v) fine behaviour of each fractional Sobolev function in \({\mathbb {R}}^n\).