Local Minimization, Variational Evolution and Γ-Convergence

• Main Author: Braides, Andrea (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Lecture Notes in Mathematics, 2094
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Approximation theory.; Functional analysis.; Partial differential equations.; Applied mathematics.; Engineering mathematics.; Calculus of variations.; Applications of Mathematics.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.; Approximations and Expansions.; Analysis.; Functional Analysis.

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...

Table of Contents:

• 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
• Index.