Ultracontractive bounds on Hamilton-Jacobi solutions
type: Item
instance of: scholarly article
title: Ultracontractive bounds on Hamilton-Jacobi solutions
zbMATH Open document ID: 1015.35019
DOI: 10.1016/S0007-4497(02)01128-4
author: Ivan Gentil
published in: Bulletin des Sciences Mathématiques
publication date: 2003-03-23T00:00:00Z
review text: The main results of this paper concern the border of three theorems, which are respectively the theorem of hypercontractivity of Gross, the theorem of hypercontractivity of Bobkov-Gentil-Ledoux and the theorem of ultracontractivity of Varopoulos. Following the equivalence between logarithmic Sobolev inequality, hypercontractivity of the heat semigroup showed by Gross and hypercontractivity of Hamilton-Jacobi equations, the author proves, like the Varopoulos theorem, the equivalence between Euclidean-type Sobolev inequality and an ultracontractive control of the Hamilton-Jacobi equations. Ultracontractive estimations under general Sobolev inequality, which imply in the particular case of probability measure transportation inequalities, are also obtained.
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 35F20
zbMATH DE Number: 1886863
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: transportation inequality
reviewed by: Vasile Iftode
MaRDI profile type: Publication
cites work: On logarithmic Sobolev inequalities. With a preface of Dominique Bakry and Michel Ledoux
cites work: Q4309937
cites work: Viscosity solutions of Hamilton-Jacobi equations
cites work: Optimal heat kernel bounds under logarithmic Sobolev inequalities
cites work: Sobolev inequalities in disguise
cites work: Hypercontractivity of Hamilton-Jacobi equations.
cites work: Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
cites work: From Brunn-Minkowski to Brascamp-Lieb and to logarithmic Sobolev inequalities
cites work: Superadditivity of Fisher's information and logarithmic Sobolev inequalities
cites work: Q4041031
cites work: Brunn-Minkowski inequality and its aftermath
cites work: Q4399897
cites work: Logarithmic Sobolev Inequalities
cites work: Constantes explicites pour les inégalités de Sobolev sur les variétés Riemanniennes compactes
cites work: The geometry of Markov diffusion generators
cites work: Bounding \(\bar d\)-distance by informational divergence: A method to prove measure concentration
cites work: A measure concentration inequality for contracting Markov chains
cites work: Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
cites work: Q3681117
cites work: Hardy-Littlewood theory for semigroups
cites work: Q4011199
description: scientific article; zbMATH DE number 1886863