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New Directions in Dirichlet Forms
Jürgen Jost, Max Planck Institute for Mathematics, Leipzig, Germany, Wilfrid Kendall, University of Warwick, Coventry, England, Umberto Mosco, University La Sapienza, Rome, Italy, Michael Röckner, University of Bielefeld, Germany, and Karl-Theodor Sturm, University of Bonn, Germany
A co-publication of the AMS and International Press.
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AMS/IP Studies in Advanced Mathematics
1998; 277 pp; hardcover
Volume: 8
ISBN-10: 0-8218-1061-8
ISBN-13: 978-0-8218-1061-3
List Price: US$60
Member Price: US$48
Order Code: AMSIP/8
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The theory of Dirichlet forms brings together methods and insights from the calculus of variations, stochastic analysis, partial differential and difference equations, potential theory, Riemannian geometry and more. This book features contributions by leading experts and provides up-to-date, authoritative accounts on exciting developments in the field and on new research perspectives. Topics covered include the following: stochastic analysis on configuration spaces, specifically a mathematically rigorous approach to the stochastic dynamics of Gibbs measures and infinite interacting particle systems; subelliptic PDE, homogenization, and fractals; geometric aspects of Dirichlet forms on metric spaces and function theory on such spaces; generalized harmonic maps as nonlinear analogues of Dirichlet forms, with an emphasis on non-locally compact situations; and a stochastic approach based on Brownian motion to harmonic maps and their regularity.

Various new connections between the topics are featured, and it is demonstrated that the theory of Dirichlet forms provides the proper framework for exploring these connections.

Titles in this series are co-published with International Press, Cambridge, MA.

Readership

Graduate students and researchers working in PDEs, calculus of variations, stochastic analysis, potential theory, Riemannian and metric geometry, fractals and homogenization.

Table of Contents

  • J. Jost -- Nonlinear Dirichlet forms
  • W. S. Kendall -- From stochastic parallel transport to harmonic maps
  • U. Mosco -- Dirichlet forms and self-similarity
  • M. Röckner -- Stochastic analysis on configuration spaces: Basic ideas and recent results
  • K.-T. Sturm -- The geometric aspect of Dirichlet forms
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