Dirichlet Forms: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna, Italy, June 8-19, 1992

by E. Fabes, Gianfausto Dell'Antonio (Editor), M. Fukushima, Umberto Mosco (Editor), L. Gross

Overview

The theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (shasticprocesses, quantum field theory, composite materials,...). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Shastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad.

Product Details

ISBN-13:	9783540574217
Publisher:	Springer Berlin Heidelberg
Publication date:	02/18/1994
Series:	Lecture Notes in Mathematics , #1563
Edition description:	1993
Pages:	252
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Gaussian upper bounds on fundamental solutions of parabolic equations; the method of nash.- Two topics related to Dirichlet forms: quasi everywhere convergences and additive functionals.- Logarithmic Sobolev inequalities and contractivity properties of semigroups.- Potential theory of non-divergence form elliptic equations.- General theory of Dirichlet forms and applications.- Logarithmic Sobolev inequalities for gibbs states.