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AuthorFabes, Eugene. author
TitleDirichlet Forms [electronic resource] : Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna, Italy, June 8-19, 1992 / by Eugene Fabes, Masatoshi Fukushima, Leonard Gross, Carlos Kenig, Michael Rรถckner, Daniel W. Stroock ; edited by Gianfausto Dell'Antonio, Umberto Mosco
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect tohttp://dx.doi.org/10.1007/BFb0074088
Descript VIII, 252 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Probabilities Mathematics Probability Theory and Stochastic Processes Analysis



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