17 sep 2001 - 24 sep 2001   [open in google calendar]

C.N.R.- Gruppo Nazionale Analisi Matematica Probabilità e Applicazioni

School on

HOMOGENIZATION TECHNIQUES AND ASYMPTOTIC METHODS FOR PROBLEMS WITH MULTIPLE SCALES

17-21 September 2001

Dipartimento di Matematica - Politecnico di Torino Corso Duca degli Abruzzi 24, Torino

Lecturers and Courses:

Andrea Braides (Università di Roma `Tor Vergata'): From discrete to continuous variational problems: an introduction

A. Defranceschi (Università di Parma): Relaxation problems for bulk and interfacial energies

G. Chechkin (University of Moscow): Homogenization in perforated domains

G. Francfort (Universite' Paris Nord): H-measures and semi-classical measures: an introduction

A. Piatnitski (University of Moscow): Random homogenization: a basic introduction

The School is part of a project of the G.N.A.M.P.A. whose aim is to analyze techniques developed from various groups of research (operating in particular in Russia, France and Italy) relative to the interaction of phenomena of homogenization with other limit procedures as dimension reduction (mathematical theories of plates and thin films), the theory of phase transitions, processes of discretization with applications both numerical and theoretical (limits of finite-difference schemes), limits of perforated domains (relaxed Dirichlet problems), limits of sets with strongly-oscillating boundaries. A great variety of instruments has been developed in order to study such problems: from G-convergence, developed both in Italy and France and in Russia, to the Gamma-convergence of De Giorgi, the compensated compactness of Murat and Tartar, from the use of Young measures, to two-scale convergence, H-convergence, etc. These techniques have often remained confined to specialistic areas, but recently interesting result have been obtained by combining these techniques, in problems where more scales are present, typically problems in which the processes hinted at above interact. In many cases new phenomena are described that are not characteristic of the single problems. As an example, homogenization methods have allowed to characterize interesting phenomena of oscillations in problems of non-convex thin films, the application of capacitary methods to the homogenization of degenerate materials have emphasized non-local phenomena, the application of the methods of the Gamma-convergence combined toYoung measures have emphasized phenomena with more scales in non convex homogenous materials, etc. In this School we give an introduction to some of the techniques developed to study oscillatory phenomena with multiple scales.

The School is mainly thought for Ph D students or researchers in the area of (applied) Analysis, but no particular background is required.

Co-ordinator of the Project: Valeria Chiado' Piat, Dipartimento di Matematica Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, e-mail: vchiado@polito.it

For registration and accomodation, please contact: vchiado@polito.it

Speakers: Andrea Braides, Chechkin, Anneliese Defranceschi, Gilles A. Francfort, Andrey Piatnitski.