Flows and functional inequalities for fractional operators
Analysis of PDEs
2016-11-30 v1
Abstract
This paper collects results concerning global rates and large time asymptotics of a fractional fast diffusion on the Euclidean space, which is deeply related with a family of fractional Gagliardo-Nirenberg-Sobolev inequalities. Generically, self-similar solutions are not optimal for the Gagliardo-Nirenberg-Sobolev inequalities, in strong contrast with usual standard fast diffusion equations based on non-fractional operators. Various aspects of the stability of the self-similar solutions and of the entropy methods like carr{\'e} du champ and R{\'e}nyi entropy powers methods are investigated and raise a number of open problems.
Cite
@article{arxiv.1611.09597,
title = {Flows and functional inequalities for fractional operators},
author = {Jean Dolbeault and An Zhang},
journal= {arXiv preprint arXiv:1611.09597},
year = {2016}
}