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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.
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