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- Carlen, Eric A.
- Department of Mathematics, Rutgers University
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- Lieb, Elliott H.
- Department of Mathematics and Physics, Princeton University
書誌事項
- タイトル別名
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- A DUAL FORM OF THE SHARP NASH INEQUALITY AND ITS WEIGHTED GENERALIZATION (Tosio Kato Centennial Conference)
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抄録
The well known duality between the Sobolev inequality and the Hardy-Littlewood-Sobolev inequality suggests that the Nash inequality should also have an interesting dual form. We provide one here. This dual inequality relates the L^{2} norm to the infimal convolution of the L^{infty} and H^{-1} norms. The computation of this infimal convolution is a minimization problem, which we solve explicitly, thus providing a new proof of the sharp Nash inequality itself. This proof, via duality, also yields the sharp form of some weighted generalizations of the Nash inequality and the dual of these weighted variants.
収録刊行物
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- 数理解析研究所講究録
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数理解析研究所講究録 2074 63-67, 2018-07
京都大学数理解析研究所
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詳細情報 詳細情報について
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- CRID
- 1050282677566142208
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- NII論文ID
- 120006645526
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- NII書誌ID
- AN00061013
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- ISSN
- 18802818
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- HANDLE
- 2433/242040
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- NDL書誌ID
- 029384017
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- NDL
- CiNii Articles