## 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, Issue 1563The 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Institut fur Angewandte Mathematik | 6 |

The Nash Method Applied to Heat Kernels on Riemannian Manifolds | 12 |

GROSS Logarithmic Sobolev Inequalities | 54 |

Copyright | |

10 other sections not shown

### Other editions - View all

Dirichlet Forms: Lectures given at the 1st Session of the Centro ... E. Fabes,M. Fukushima,L. Gross,C. Kenig,M. Röckner,D.W. Stroock No preview available - 1993 |

Dirichlet Forms: Lectures given at the 1st Session of the Centro ... E. Fabes,M. Fukushima,L. Gross,C. Kenig,M. Röckner,D.W. Stroock No preview available - 2014 |

### Common terms and phrases

addition adjoint Anal appear applications argument associated assume Banach space Borel boundary bounded Brownian motion called Chapter choose closed coefficients compact condition consequence consider constant contraction convergence Corollary corresponding defined Definition denote dense depending derive differential diffusion dimensional Dirichlet forms domain e~tH element elliptic equality equations equivalent estimates example exists extended fact finite fixed follows Funct function give given Hence holds hypercontractivity implies infinite integral introduce Lecture Lemma limit logarithmic Sobolev inequalities Math maximum measure non-negative norm normalized Note obtain operator particular positive potential preprint principle probability proof Proposition prove refer regular Remark replaced resolvent respect satisfies semigroup sense separable smooth solutions space stochastic differential equations strongly continuous subset Suppose symmetric Theorem theory unique zero