Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

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

Research output: Contribution to journalArticleResearchpeer-review

34 Citations (Scopus)


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 languageEnglish
Pages (from-to)19696-19701
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number46
Publication statusPublished - 16 Nov 2010


  • Gagliardo-Nirenberg-Sobolev
  • Gradient flow


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