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

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The theory of Dirichlet forms has witnessed recently some very important

developments both in theoretical foundations and in applications (stochasticprocesses, 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: - Stochastic 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.