Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

Eric A. Carien; José A. Carrillo; Michael Loss

doi:10.1073/pnas.1008323107

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

Eric A. Carien, José A. Carrillo, Michael Loss

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

34 Citations (Scopus)

Abstract

We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥ 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.

Original language	English
Pages (from-to)	19696-19701
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	107
Issue number	46
DOIs	https://doi.org/10.1073/pnas.1008323107
Publication status	Published - 16 Nov 2010

Keywords

Gagliardo-Nirenberg-Sobolev
Gradient flow

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title = "Hardy-Littlewood-Sobolev inequalities via fast diffusion flows",

abstract = "We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥ 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.",

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author = "Carien, {Eric A.} and Carrillo, {Jos{\'e} A.} and Michael Loss",

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AU - Carien, Eric A.

AU - Carrillo, José A.

AU - Loss, Michael

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N2 - We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥ 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.

AB - We give a simple proof of the λ = d - 2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d ≥ 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d = 2 via a monotone flow governed by the fast diffusion equation.

KW - Gagliardo-Nirenberg-Sobolev

KW - Gradient flow

U2 - 10.1073/pnas.1008323107

DO - 10.1073/pnas.1008323107

M3 - Article

SN - 0027-8424

VL - 107

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EP - 19701

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

IS - 46

ER -

Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

Abstract

Keywords

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