Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

Details Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

2010-06-11

arxiv.org/abs/1006.2255v1

Mathematics

Analysis of PDEs

Scientific paper

We give a simple proof of the $\lambda = d-2$ 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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