Felix Leinen, ohannes Gutenberg-Universität (Mainz, Germania) Teoria asintotica dei caratteri e C*-algebre Tuesday, March 02 2004, at 17:00 Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza |
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Alberto Perelli, Università di Genova Funzioni L: la classe di Selberg Monday, February 16 2004, at 17:00 Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza | |
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Thierry Coulhon, Université de Cergy-Pontoise (Cergy, France) Characterization of sub-Gaussian heat kernel estimates on strongly recurrent graphs Monday, January 19 2004, at 17:00 Dipartimento di Matematica - Università degli Studi - Via Saldini 50 - Milano - Sala di Rappresentanza |
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Klaus Engel, Università de L'Aquila Semigruppi di operatori per equazioni di evoluzione Wednesday, December 10 2003, at 17:00 Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Aula 3 (piano terra) |
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Miroslav Silhavy, Akademie ved Ceske Republiky, Praha (Rep. Ceca) Fluxes of mechanical quantities across fractal boundaries Wednesday, December 03 2003, at 17:00 Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza |
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Abstract
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This seminar deals with fluxes of quantities across parts of the boundary of a body R with fractal boundary. A broad interpretation of the notion of a fractal boundary is employed here to mean any bounded subset R of Rn whose boundary dR is so complicated that the outer normal n to R is not defined for a.e. point of dR. Here a.e. means almost everywhere with respect to the n-1 dimensional Hausdorff measure (area) Hn-1. For a fractal body, Hn-1(dR) is infinite, since otherwise R is a set of finite perimeter with an Hn-1 a.e. defined normal. The paper is concerned with determining the net flux F(q,T) of a scalar quantity (such as the heat flux) across a subset T of dR, where the quantity is represented by a continuous field of the flux vector q on Rn with integrable distributional divergence. The paper examines basic properties of the functional F: (1) On the negative side, it is shown that if Hn-1(dR) is infinite, then F(q, . ) does not extend to a measure unless q is in some sense trivial. (2) On the positive side, it is proved that each R can be approximated by a sequence Rj of sets of finite perimeter such that the classical Cauchy formula holds in some limiting sense. (3) Consequences are derived of the situation when a given T insulates under q in the sense that the flux through each trace S of T vanishes. (4) Conditions are given on dR for the locality of F (so that the value F(q,T) depends on the values of q on T). (5) Classes of flux vector fields are described to which F(q,T) can be extended. |
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Fulvio Ricci, Scuola Normale Superiore (Pisa) Struttura riemanniana e sub-riemanniana sul gruppo di Heisenberg e analisi dei rispettivi (sub-)laplaciani Monday, November 17 2003, at 15:30 Dipartimento di Matematica e Applicazioni - Università degli Studi di Milano Bicocca - Via Bicocca degli Arcimboldi, 8 |
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