Braides A. Local Minimization, Variational Evolution and Γ-Convergence

Springer, 2014. — 184 p.This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.Front Matter
Introduction
Global Minimization
Parameterized Motion Driven by Global Minimization
Local Minimization as a Selection Criterion
Convergence of Local Minimizers
Small-Scale Stability
Minimizing Movements
Minimizing Movements Along a Sequence of Functionals
Geometric Minimizing Movements
Different Time Scales
Stability Theorems
Back Matter