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arXiv · 1006.2255

Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

Eric A. Carlen·Jose Antonio Carrillo·Michael Loss
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Abstract

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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Eric A. Carlen, Jose Antonio Carrillo, Michael Loss. 2010-06-11. Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows. https://doi.org/10.1073/pnas.1008323107

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