Calculus of Variations. 1st ed. 2018

種類:

電子ブック

責任表示:

by Filip Rindler

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Rindler, Filip.
• SpringerLink (Online service)

シリーズ名:

Universitext ;

ISBN:

9783319776378 [3319776371]    

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

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