TY  - BOOK
AU  - Bakry, Dominique
AU  - Gentil, Ivan
TI  - Analysis and Geometry of Markov Diffusion Operators
T2  - Grundlehren der mathematischen Wissenschaften 348
SN  - 9783319002262
PY  - 2014///
CY  - Switzerland
PB  - Springer International Publishing
KW  - Markov Diffusion Operators
N1  - A  Series of Comprehensive Studies in Mathematics; Markov Semigroups, Basic and Examples
Three Model Functional Inequalities
Related Functional, Isoperimetric and Transportation Inequalities
N2  - The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations.

The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium andgeometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic
ER  -