Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.

Carlen, Eric A; Carrillo, José A; Loss, Michael · Proc Natl Acad Sci U S A · 2010

basic_science · Level V

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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.