Calculus of Variations / by Filip Rindler

Von:

Rindler, Filip [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Universitext | Springer eBook Collection | SpringerLink BücherVerlag: Cham : Springer International Publishing, 2018Beschreibung: Online-Ressource (XII, 444 p. 36 illus., 2 illus. in color, online resource)ISBN:

9783319776378

Schlagwörter:

Genre/Form:

Lehrbuch

Andere physische Formen: 9783319776361 | Erscheint auch als: Calculus of variations. Cham, Switzerland : Springer, 2018. xii, 444 Seiten | Printed edition: 9783319776361 DDC-Klassifikation:

515.64

MSC: MSC: *49-01 | 49J40 | 90C90 | 47J20 | 90C31 | 47E05 | 62P30RVK: RVK: SK 660LOC-Klassifikation:

QA315-316 QA402.3 QA402.5-QA402.6
QA315-316
QA402.3
QA402.5-QA402.6

DOI: DOI: 10.1007/978-3-319-77637-8Online-Ressourcen:

Zusammenfassung: This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendixZusammenfassung: Part I Basic Course -- 1 Introduction -- 2 Convexity -- 3 Variations -- 4 Young Measures -- 5 Quasiconvexity -- 6 Polyconvexity -- 7 Relaxation -- Part II Advanced Topics -- 8 Rigidity -- 9 Microstructure -- 10 Singularities -- 11 Linear-Growth Functionals -- 12 Generalized Young Measures -- 13 G-Convergence -- A Prerequisites -- References -- IndexPPN: PPN: 1026858186Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS

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