Dirichlet Forms

The theory of Dirichlet forms has witnessed recently somevery 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.

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.