Hardy-Littlewood-Sobolev inequalities via fast diffusion flows.

Author: 

Carlen, E
Carrillo, J
Loss, M

Publication Date: 

November 2010

Journal: 

Proceedings of the National Academy of Sciences of the United States of America

Last Updated: 

2020-10-31T07:59:14+00:00

Issue: 

46

Volume: 

107

DOI: 

10.1073/pnas.1008323107

page: 

19696-19701

abstract: 

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.

Symplectic id: 

1098045

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article