03036i0n a2200337 4500 u7433 SIRSI 20251112200007.0 |a250827s2018 gw | r 0001|00eng d 9783319776361 MiAaPQ eng rda pn MiAaPQ MiAaPQ clrauoh Rindler, Filip. author Calculus of Variations / Filip Rindler. First edition: 2018. Cham : Springer International Publishing : Imprint: Springer, 2018. Universitext, 0172-5939 text txt rdacontent unmediated n rdamedia volume nc rdacarrier 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. Calculus of variations. Partial differential equations. Functional analysis. Mathematical physics. Calculus of Variations and Optimal Control Optimization.|0https://scigraph.springernature.com/ontologies/product-market-codes/M26016 Partial Differential Equations.|0https://scigraph.springernature.com/ontologies/product-market-codes/M12155 Functional Analysis.|0https://scigraph.springernature.com/ontologies/product-market-codes/M12066 Mathematical Applications in the Physical Sciences.|0https://scigraph.springernature.com/ontologies/product-market-codes/M13120 6449 6449 2026-04-29 14:19:47 35672004987 1 515.64 R579c 2018 35672004987 2026-04-02 1 2025-10-14 BOOK 0 0 0 COL_GRAL 0 BCENTRAL BCENTRAL 2025-08-27