Paper Info
Title
The information-theoretic meaning of Gagliardo–Nirenberg type inequalities
Abstract
Gagliardo-Nirenberg inequalities are interpolation inequalities which were proved independently by Gagliardo and Nirenberg in the late fifties. In recent years, their connections with theoretic aspects of information theory and nonlinear diffusion equations allowed to obtain some of them in optimal form, by recovering both the sharp constants and the explicit form of the optimizers. In this note, at the light of these recent researches, we review the main connections between Shannon-type entropies, diffusion equations and a class of these inequalities.
Year
DOI
Venue
2018
10.4171/RLM/845
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI
Keywords
DocType
Volume
Heat equation,nonlinear diffusions,Shannon entropy,Renyi entropy,Fisher-type informations,Gagliardo-Nirenberg type inequalities
Journal
30
Issue
ISSN
Citations 
2
1120-6330
1
PageRank 
References 
Authors
0.36
10
1
Name
Order
Citations
PageRank
Giuseppe Toscani113824.06