TY  - DATA
AU  - Rindler, Filip.
TI  - Calculus of Variations
SN  - 9783319776378
U1  - 519.6 23
PY  - 2018///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematical optimization
KW  - Calculus of variations
KW  - Differential equations
KW  - Functional analysis
KW  - Mathematical physics
KW  - Calculus of Variations and Optimization
KW  - Differential Equations
KW  - Functional Analysis
KW  - Mathematical Physics
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-77637-8
ER  -