Flows and functional inequalities for fractional operators

2016/11/29 by Jean Dolbeault, An Zhang, Dolbeault, Jean +1 · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering

paper · doi:10.48550/arxiv.1611.09597

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 carré du champ and Rényi entropy powers methods are investigated and raise a number of open problems.

Cited by

• Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities

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