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Acta Mathematica Scientia

, Volume 39, Issue 1, pp 26–36 | Cite as

Hardy’S Inequalities with Maximizers for W1,p Functions on Bounded Star Domains

  • Ahmed A. AbdelhakimEmail author
Article
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Abstract

With the help of a radially invariant vector field, we derive inequalities of the Hardy kind, with no boundary terms, for W1,p functions on bounded star domains. Our results are not obtainable from the classical inequalities for W01,p functions. Unlike in W01,p, our inequalities admit maximizers that we describe explicitly.

Key words

Hardy type inequalities radially invariant vector field Sobolev maximizers star domains trace operator 

2010 MR Subject Classification

35A23 26D15 46E35 

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Notes

Acknowledgements

The author is grateful to Craig Cowan at the university of Manitoba for his valuable comments on the counterexample that proves Proposition 2.1.

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Copyright information

© Wuhan Institutes of Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceAssiut UniversityAssiutEgypt

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