数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (1): 26-36.doi: 10.1007/s10473-019-0103-z

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HARDY’S INEQUALITIES WITH MAXIMIZERS FOR W1,p FUNCTIONS ON BOUNDED STAR DOMAINS

Ahmed A. ABDELHAKIM   

  1. Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt
  • 收稿日期:2018-01-18 出版日期:2019-02-25 发布日期:2019-11-14
  • 作者简介:Ahmed A. ABDELHAKIM,E-mail:ahmed.abdelhakim@aun.edu.eg

HARDY’S INEQUALITIES WITH MAXIMIZERS FOR W1,p FUNCTIONS ON BOUNDED STAR DOMAINS

Ahmed A. ABDELHAKIM   

  1. Department of Mathematics, Faculty of Science, Assiut University, 71516 Assiut, Egypt
  • Received:2018-01-18 Online:2019-02-25 Published:2019-11-14

摘要: With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W 1,p functions on bounded star domains. Our results are not obtainable from the classical inequalities for W1,p functions. Unlike in W1,p, our inequalities admit maximizers that we describe explicitly.

关键词: Hardy type inequalities, radially invariant vector field, Sobolev maximizers, star domains, trace operator

Abstract: With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W 1,p functions on bounded star domains. Our results are not obtainable from the classical inequalities for W1,p functions. Unlike in W1,p, our inequalities admit maximizers that we describe explicitly.

Key words: Hardy type inequalities, radially invariant vector field, Sobolev maximizers, star domains, trace operator