Published in

Oxford University Press (OUP), International Mathematics Research Notices, p. rnv131

DOI: 10.1093/imrn/rnv131

Links

Tools

Export citation

Search in Google Scholar

Stability Results for Logarithmic Sobolev and Gagliardo–Nirenberg Inequalities

Journal article published in 2015 by Jean Dolbeault ORCID, Giuseppe Toscani
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Upload
Green circle
Postprint: archiving allowed
Upload
Red circle
Published version: archiving forbidden
Policy details
Data provided by SHERPA/RoMEO

Abstract

This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit stability measurements, i.e., bound with explicit constants distances to the manifold of optimal functions. Various results are obtained for the Gaussian logarithmic Sobolev inequality and its Euclidean counterpart, for the Gaussian generalized Poincar{é} inequalities and for the Gagliardo-Nirenberg inequalities. As a consequence, faster convergence rates in diffusion equations (fast diffusion, Ornstein-Uhlenbeck and porous medium equations) are obtained.