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The Best Constant in the Embedding of WN,1( N ) into \(L^{\infty }(\mathbb {R} ^{N})\)

  • Itai Shafrir
Article

Abstract

We compute the best constant in the embedding of \(W^{N,1}(\mathbb {R} ^{N})\) into \(L^{\infty }(\mathbb {R} ^{N})\), extending a result of Humbert and Nazaret in dimensions one and two to any N. The main tool is the identification of \(\log |x|\) as a fundamental solution of a certain elliptic operator of order 2N.

Keywords

Best constant Sobolev embedding 

Mathematics Subject Classification (2010)

Primary 46E35 Secondary 35A23 

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Notes

Acknowledgments

The author was supported by the Israel Science Foundation (Grant No. 999/13). Part of this work was done while he was visiting the University Claude Bernard Lyon 1. He thanks the Mathematics Department for its hospitality.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsTechnion - I.I.T.HaifaIsrael

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