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Titlebook: Local Minimization, Variational Evolution and Γ-Convergence; Andrea Braides Book 2014 Springer International Publishing Switzerland 2014 4

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发表于 2025-3-21 20:02:46 | 显示全部楼层 |阅读模式
书目名称Local Minimization, Variational Evolution and Γ-Convergence
编辑Andrea Braides
视频video
概述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 dire
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Local Minimization, Variational Evolution and Γ-Convergence;  Andrea Braides Book 2014 Springer International Publishing Switzerland 2014 4
描述.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..
出版日期Book 2014
关键词49J45,74Q10,49J40,74Q05; Gamma-convergence; Gradient flow; Homogenization; Local minimization; Variationa
版次1
doihttps://doi.org/10.1007/978-3-319-01982-6
isbn_softcover978-3-319-01981-9
isbn_ebook978-3-319-01982-6Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer International Publishing Switzerland 2014
The information of publication is updating

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发表于 2025-3-21 20:56:51 | 显示全部楼层
发表于 2025-3-22 03:54:17 | 显示全部楼层
Minimizing Movements Along a Sequence of Functionals,ements coincide with the one of the Mumford–Shah functional, while for oscillating energies we have a critical .-. regime, in which we show phenomena of pinning, non-uniqueness and homogenization of the velocity. In this example, the case . gives an effective motion, from which the ones in all regimes can be deduced, including the extreme ones.
发表于 2025-3-22 06:49:04 | 显示全部楼层
Geometric Minimizing Movements,motion showing pinning for large sets and a discontinuous dependence of the velocity on the curvature. Additional effects are shown to appear for minimizing movements related to the homogenization of perimeter functionals with oscillating forcing terms.
发表于 2025-3-22 12:01:01 | 显示全部楼层
Small-Scale Stability,n energy barrier of a specified height. This notion is a quantification of the notion of local minimizer, which instead is “scale-independent” and will allow us to state a convergence theorem for sequences of stable points. Even though a general result is not available, we will show how .-converging sequences often give rise to stable convergence.
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Different Time Scales,s, or the gradient theory of phase transitions. These are obtained by suitably choosing a diverging (but positive) scaling of the energies. Negative scalings may be used to define a backward motion of some energy ., after properly choosing a family of functional .-converging to ..
发表于 2025-3-23 01:47:55 | 显示全部楼层
Book 2014nal 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 converg
发表于 2025-3-23 08:46:08 | 显示全部楼层
Book 2014vement 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..
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