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Mathematics - Applications | Local Minimization, Variational Evolution and Γ-Convergence

Local Minimization, Variational Evolution and Γ-Convergence

Series: Lecture Notes in Mathematics, Vol. 2094

Braides, Andrea

2014, XI, 174 p. 42 illus.

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  • Provides connections between topics of active current research
  • Presents the subjects with examples from the main areas that have made Gamma-convergence so successful
  • Proposes numerous examples of directions of further research

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.

Content Level » Research

Keywords » 49J45,74Q10,49J40,74Q05 - Gamma-convergence - Gradient flow - Homogenization - Local minimization - Variational Evolution

Related subjects » Analysis - Applications - Dynamical Systems & Differential Equations - Mathematics

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