Functional Inequalities and Hamilton-Jacobi Equations in Geodesic Spaces

被引：17

作者：

Balogh, Zoltan M. ^{[1
]}

Engulatov, Alexandre ^{[1
]}

Hunziker, Lars ^{[2
]}

Maasalo, Outi Elina ^{[1
]}

机构：

[1] Univ Bern, Inst Math, CH-3012 Bern, Switzerland

[2] Univ Technol Sydney, Dept Math, Sydney, NSW 2007, Australia

来源：

POTENTIAL ANALYSIS | 2012年 / 36卷 / 02期

关键词：

Logarithmic-Sobolev inequalites; Talagrand inequalites; Hamilton-Jacobi semigroup; Poincare inequalities; Geodesic metric space; Metric-measure space; METRIC-MEASURE-SPACES; HOPF-LAX FORMULA; TRANSPORTATION COST; BRASCAMP; GEOMETRY; MAPS;

D O I：

10.1007/s11118-011-9232-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the connection between the p-Talagrand inequality and the q-logarithmic Sololev inequality for conjugate exponents p >= 2, q <= 2 in proper geodesic metric spaces. By means of a general Hamilton-Jacobi semigroup we prove that these are equivalent, and moreover equivalent to the hypercontractivity of the Hamilton-Jacobi semigroup. Our results generalize those of Lott and Villani. They can be applied to deduce the p-Talagrand inequality in the sub-Riemannian setting of the Heisenberg group.

引用

页码：317 / 337

页数：21

共 30 条

[1]

Ambrosio L., 2000, SELECTED TOPICS ANAL

[2]

Bakry D., 1985, SEM PROB 19, V1123, P177

[3] Mass transport and variants of the logarithmic sobolev inequality [J].