Topics on Concentration Phenomena and Problems with Multiple Scales - Lecture Notes of the Unione Matematica Italiana 2006 edition

Marc Notes: Includes bibliographical references and index. Table of Contents: Problems with multiple scales.- From discrete systems to continuous variational problems: an introduction.- Relaxation for bulk and interfacial energies.- Convergence of Dirichlet forms on fractals.- Homogenization in perforated domains.- Homogenization of random non stationary parabolic operators.- Problems with concentration.- ?-convergence for concentration problems.- Gamma-convergence of gradient flows and applications to Ginzburg-Landau vortex dynamics.- PDE analysis of concentrating energies for the Ginzburg-Landau equation. Publisher Marketing: The research group Homogenization Techniques and Asymptotic Methods for Problems with Multiple Scales, co-ordinated by Valeria Chiad o Piat and funded by INdAM-GNAMPA (Istituto Nazionale di Alta Matematica-Gruppo Nazionale per l Analisi Matematica, la Probabilit a e le loro Applicazioni), - erated from 2001 to 2005, involving in its activities a number of young Italian mathematicians, mainly interested in problems in the Calculus of Variations and Partial Di?erential Equations. One of the initiatives of that group has been the organization of a number of schools. Those in the years 2001-2003, whose lecture notes are gathered in this book, had been devoted to problems with oscillations and concentrations, while the schools in the years 2004-2005 covered a range of topics of Applied Mathematics. The ?rst school in Turin, 17 21 September 2001, bearing the name of the research group and devoted to problems with multiple scales, was partially disrupted by the events of September 11 of that year, one speaker, Gilles Francfort, ?nding himself grounded in Los Angeles, and two other speakers, Andrey Piatnitski and Gregory Chechkin, slowed down in their car trip to Italy by the tightening of the borders around the European Community. The two remaining speakers managed however to enlarge their courses to cover some extra material, encouraged by the receptive audience."

Contributor Bio:  Braides, Andrea Braides is with SISSA.