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Calculus of variations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Calculus of variations/ by Filip Rindler.
Author:	Rindler, Filip.
Published:	Cham :Springer International Publishing : : 2018.,
Description:	xii, 444 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Calculus of variations. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-77637-8
ISBN:	9783319776378

Calculus of variations
Rindler, Filip.

Calculus of variations[electronic resource] /by Filip Rindler. - Cham :Springer International Publishing :2018. - xii, 444 p. :ill. (some col.), digital ;24 cm. - Universitext,0172-5939. - Universitext..

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.

ISBN: 9783319776378

Standard No.: 10.1007/978-3-319-77637-8doiSubjects--Topical Terms:

527927
Calculus of variations.

LC Class. No.: QA315 / .R563 2018

Dewey Class. No.: 515.64

Calculus of variations
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100 1 $a Rindler, Filip. $3 1206420
245 1 0 $a Calculus of variations $h [electronic resource] / $c by Filip Rindler.
260 $a Cham : $c 2018. $b Springer International Publishing : $b Imprint: Springer,
300 $a xii, 444 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a 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.
520 $a 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.
650 0 $a Calculus of variations. $3 527927
650 1 4 $a Mathematics. $3 527692
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 593942
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Functional Analysis. $3 672166
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
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