000 03036i0n a2200337 4500
001 u7433
003 SIRSI
005 20251112200007.0
008 |a250827s2018 gw | r 0001|00eng d
020 _a9783319776361
040 _aMiAaPQ
_beng
_erda
_epn
_cMiAaPQ
_dMiAaPQ
_dclrauoh
100 _aRindler, Filip.
_eauthor
245 1 0 _aCalculus of Variations /
_cFilip Rindler.
250 _aFirst edition: 2018.
264 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
440 _aUniversitext,
_x0172-5939
336 _atext
_btxt
_2rdacontent
337 _aunmediated
_bn
_2rdamedia
338 _avolume
_bnc
_2rdacarrier
500 _aPart 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 _aThis 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 _aCalculus of variations.
650 _aPartial differential equations.
650 _aFunctional analysis.
650 _aMathematical physics.
650 _aCalculus of Variations and Optimal Control
650 _aOptimization.|0https://scigraph.springernature.com/ontologies/product-market-codes/M26016
650 _aPartial Differential Equations.|0https://scigraph.springernature.com/ontologies/product-market-codes/M12155
650 _aFunctional Analysis.|0https://scigraph.springernature.com/ontologies/product-market-codes/M12066
650 _aMathematical Applications in the Physical Sciences.|0https://scigraph.springernature.com/ontologies/product-market-codes/M13120
999 _c6449
_d6449