Local Minimization, Variational Evolution and Γ-Convergence
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Beschreibung
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.
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.
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 Includes supplementary material: sn.pub/extras
Autor*in
Andrea Braides
Themen in »Local Minimization, Variational Evolution and Γ-Convergence«
49J45,74Q10,49J40,74Q05 Gamma-convergence Gradient flow Homogenization Local minimization Variational Evolution partial differential equations
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“The volume is carefully written and the material is organized in such a way that a Ph.D. student can gradually become familiar with Γ-convergence analysis and related tools. When possible, one-dimensional examples are chosen to illustrate the topics and several figures help the reader follow the presentation. The volume is very suitable for a Ph.D. course devoted to an audience with a good background in functional analysis, function spaces, and variational problems.” (Giuseppe Buttazzo, Mathematical Reviews, August, 2014)
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