Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA.
Proc Natl Acad Sci U S A. 2010 Nov 16;107(46):19696-701. doi: 10.1073/pnas.1008323107. Epub 2010 Nov 1.
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.
我们通过由快速扩散方程控制的单调流，给出了 d≥3 时 sharp Hardy-Littlewood-Sobolev 不等式的 λ=d-2 情形和 d=2 时 sharp Logarithmic Hardy-Littlewood-Sobolev 不等式的一个简单证明。
