<電子ブック>
Calculus of Variations / by Filip Rindler
(Universitext. ISSN:21916675)
版 | 1st ed. 2018. |
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出版者 | (Cham : Springer International Publishing : Imprint: Springer) |
出版年 | 2018 |
本文言語 | 英語 |
大きさ | XII, 444 p. 36 illus., 2 illus. in color : online resource |
著者標目 | *Rindler, Filip author SpringerLink (Online service) |
件 名 | LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations LCSH:Functional analysis LCSH:Mathematical physics FREE:Calculus of Variations and Optimization FREE:Differential Equations FREE:Functional Analysis FREE:Mathematical Physics |
一般注記 | 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 -- Index 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 appendix HTTP:URL=https://doi.org/10.1007/978-3-319-77637-8 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783319776378 |
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電子リソース |
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EB00229965 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA402.5-402.6 LCC:QA315-316 DC23:519.6 DC23:515.64 |
書誌ID | 4000118326 |
ISBN | 9783319776378 |
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