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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.
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