Topics on Concentration Phenomena and Problems with Multiple Scales

• Corporate Author: SpringerLink (Online service)
• Other Authors: Braides, Andrea (Editor), Piat, Valeria Chiadò (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes of the Unione Matematica Italiana, 2
• Subjects: Mathematics.; Measure theory.; Partial differential equations.; Functions of real variables.; Calculus of variations.; Calculus of Variations and Optimal Control; Optimization.; Measure and Integration.; Partial Differential Equations.; Real Functions.

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 separa...

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.