Geometric Flows on Planar Lattices
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Beschreibung
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
Introduces important concepts in modern Applied Analysis through prototypical problems, discussed in a natural way Advanced research topics are introduced in a stimulating and constructive fashion Copious figures promote visual descriptions of concepts and methods
Autor*in
Andrea Braides
Themen in »Geometric Flows on Planar Lattices«
Variational evolution Gradient flows Homogenization Heterogeneous media Geometric motions Motion by crystalline curvature Discrete-to-continuum limits for lattice energies Evolution of microstructure Sets of finite perimeter Interfacial energies
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“The book fairly self-contained. Many illuminating examples are worked out in detail, and a large number of extensions are included." (John Urbas, zbMATH 1486.53002, 2022)
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