Canceling effects in higher-order Hardy–Sobolev inequalities

详细信息    查看全文

• 作者：Andrea Cianchi ; Norisuke Ioku
• 关键词：Mathematics Subject Classification46E35 ; 46E30
• 刊名：Calculus of Variations and Partial Differential Equations
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：56
• 期：2
• 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

A classical first-order Hardy–Sobolev inequality in Euclidean domains, involving weighted norms depending on powers of the distance function from their boundary, is known to hold for every, but one, value of the power. We show that, by contrast, the missing power is admissible in a suitable counterpart for higher-order Sobolev norms. Our result complements and extends contributions by Castro and Wang (Calc Var 39(3–4):525–531, 2010), and Castro et al. (Comptes Rendus Math Acad Sci Paris 349:765–767, 2011; J Eur Math Soc 15:145–155, 2013), where a surprising canceling phenomenon underling the relevant inequalities was discovered in the special case of functions with derivatives in \(L^1\).