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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	19696-19701
Revista	Proceedings of the National Academy of Sciences of the United States of America
Volum	107
Número	46
DOIs	https://doi.org/10.1073/pnas.1008323107
Estat de la publicació	Publicada - 16 de nov. 2010

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10.1073/pnas.1008323107

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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.",

keywords = "Gagliardo-Nirenberg-Sobolev, Gradient flow",

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

year = "2010",

month = nov,

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doi = "10.1073/pnas.1008323107",

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journal = "Proceedings of the National Academy of Sciences of the United States of America",

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T1 - Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

AU - Carien, Eric A.

AU - Carrillo, José A.

AU - Loss, Michael

PY - 2010/11/16

Y1 - 2010/11/16

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

SP - 19696

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

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