English

Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

Analysis of PDEs 2015-05-19 v1

Abstract

We give a simple proof of the λ=d2\lambda = d-2 cases of the sharp Hardy-Littlewood-Sobolev inequality for d3d\geq 3, and the sharp Logarithmic Hardy-Littlewood-Sobolev inequality for d=2d=2 via a monotone flow governed by the fast diffusion equation.

Cite

@article{arxiv.1006.2255,
  title  = {Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows},
  author = {Eric A. Carlen and Jose Antonio Carrillo and Michael Loss},
  journal= {arXiv preprint arXiv:1006.2255},
  year   = {2015}
}
R2 v1 2026-06-21T15:34:55.463Z