Hardy-Littlewood-Sobolev Inequalities via Fast Diffusion Flows

Abstract

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

References in corpus (1)

• Asymptotics of the fast diffusion equation via entropy estimates

Cited by in corpus (10)

• Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation
• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
• Sharp reversed Hardy-Littlewood-Sobolev inequality on ${\mathbb{R}}^n$
• Reverse Hardy-Littlewood-Sobolev inequalities
• The weighted ${\sigma }_k$-curvature of a smooth metric measure space
• A fractional Yamabe flow and some applications
• Stein-Weiss inequalities with the fractional Poisson kernel
• An optimal Hardy-Littlewood-Sobolev inequality on ${\mathbf{R}}^{n-k}\times {\mathbf{R}}^n$ and its consequences
• Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group
• Generalized logarithmic Hardy-Littlewood-Sobolev inequality