Local Minimization, Variational Evolution and Γ-Convergence

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Local Minimization, Variational Evolution and Γ-Convergence by Andrea Braides, Springer International Publishing
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Author: Andrea Braides ISBN: 9783319019826
Publisher: Springer International Publishing Publication: July 8, 2014
Imprint: Springer Language: English
Author: Andrea Braides
ISBN: 9783319019826
Publisher: Springer International Publishing
Publication: July 8, 2014
Imprint: Springer
Language: English

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.

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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.

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