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.
Rezensionen / Stimmen
"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)
"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)
Produkt-Info
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
62
1 farbige Abbildung, 62 s/w Abbildungen
X, 134 p. 63 illus., 1 illus. in color.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 9 mm
Gewicht
ISBN-13
978-3-030-69919-2 (9783030699192)
DOI
10.1007/978-3-030-69917-8
Schweitzer Klassifikation
Andrea Braides is professor of Mathematical Analysis at the University of Rome Tor Vergata. He is the author among others of the books Gamma-convergence for Beginners and (with A.Defranceschi) Homogenization of Multiple Integrals. He was an invited speaker at the 2014 International Congress of Mathematicians in Seoul in the section Mathematics in Science and Technology.Margherita Solci is professor of Mathematical Analysis at the University of Sassari at Alghero. She works on various topics involving variational convergence; in particular, static and dynamic passages from discrete to continuum.
Andrea Braides is professor of Mathematical Analysis at the University of Rome Tor Vergata. He is the author among others of the books Gamma-convergence for Beginners and (with A.Defranceschi) Homogenization of Multiple Integrals. He was an invited speaker at the 2014 International Congress of Mathematicians in Seoul in the section Mathematics in Science and Technology.
Margherita Solci is professor of Mathematical Analysis at the University of Sassari at Alghero. She works on various topics involving variational convergence; in particular, static and dynamic passages from discrete to continuum.
- Introduction: Motion on Lattices. - Variational Evolution. - Discrete-to-Continuum Limits of Planar Lattice Energies. - Evolution of Planar Lattices. - Perspectives: Evolutions with Microstructure.
