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

http://cvgmt.sns.it/event/115/