Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

preprint2010arXivOpen access

We give a simple proof of the $λ= d-2$ cases of the sharp Hardy-Littlewood-Sobolev inequality for $d\geq 3$ , 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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Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

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