SPONSORS: The school is co-sponsored by the GNAMPA-INdAM Project "Homogenization techniques and asymptotic methods for multiple-scale problems" (co-ordinator: V. Chiado' Piat) and by COFIN 2002 through the National Project "Calcolo delle Variazioni" (Rome Local Unit co-ordinated by A.Braides and Milano Politecnico Local Unit co-ordinated by F.Tomarelli).

ORGANIZATION: GNAMPA Project "Homogenization techniques and asymptotic methods for multiple-scale problems" (co-ordinator: V. Chiado' Piat) and the Rome Local Unit of the National Project " Calcolo delle Variazioni" (co-ordinator: A. Braides)

Lecturers and Courses:

G. ALBERTI (University of Pisa): Concentration phenomena for functionals of Ginzburg-Landau type. A variational approach.

A. GARRONI (University of Roma La Sapienza): Gamma-convergence for concentration problems with critical growth.

D. SMETS (University Pierre et Marie Curie, Paris): Shape and evolution of concentration sets in some Ginzburg-Landau-type equations.

H. M. SONER (Koc University, Istanbul): Jacobian and the Ginzburg-Landau energy.

Abstract of courses

Venue: Aula Picone, Dipartimento di Matematica 'G.Castelnuovo', Università di Roma 'La Sapienza'
(in case of too much heat: in Aula Consiglio !)

Scope of the School The aim of the School is mainly to provide an introductive presentation to some concentration phenomena arising in different situations, as variational and dynamical problems related to the Ginzburg-Landau functional, non-linear variational problems with critical growth related to the Sobolev inequality, free-boudary problems, as the so-called Bernoulli problem, related to the isoperimetric inequality for the capacity, and so on. More generally, the School is part of the project "Homogenization techniques and asymptotic methods for multiple-scale problems", of G.N.A.M.P.A-INdAM. whose aim is to analyze different techniques involved in the interaction of phenomena of homogenization type 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. In this respect, the scheduled lectures may shed some light on the interaction of techniques that are typical of the Calculus of Variations, like Gamma-convergence theory, with methods which are peculiar of Nonlinear Analysis, as the Concentration-compactness Alternative, and others.

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

Further information Contact V. Chiadò Piat ( or A. Braides (

Registration There is no registration fee but interested people are requested to register by filling the form below and sending it by e-mail to: .

Support Limited funds are available.



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