The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Lecture Notes of the Unione Matematica Italiana
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Editorial Board Franco Brezzi (Editor in Chief) Dipartimento di Matematica Università di Pavia Via Ferrata 1 27100 Pavia, Italy e-mail:
[email protected]
Persi Diaconis Department of Statistics Stanford University Stanford, CA 94305-4065, USA e-mail:
[email protected],
[email protected]
John M. Ball Mathematical Institute 24-29 St Giles' Oxford OX1 3LB United Kingdom e-mail:
[email protected]
Nicola Fusco Dipartimento di Matematica e Applicazioni Università di Napoli "Federico II", via Cintia Complesso Universitario di Monte S.Angelo 80126 Napoli, Italy e-mail