Hardy-Littlewood-Sobolev inequalities via fast diffusion flows

摘要

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.