000			02746nmm a22003135i 4500
005			20230705150634.0
008			180619s2018 sz | s |||| 0|eng d
020			_a9783319776378 _9978-3-319-77637-8
082			_a519.6 _223
082			_a515.64 _223
100			_aRindler, Filip. _920280
245			_aCalculus of Variations _h[electronic resource] / _cby Filip Rindler.
250			_a1st ed. 2018.
260			_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2018.
300			_aXII, 444 p. 36 illus., 2 illus. in color. _bonline resource.
505			_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			_aMathematical optimization. _920281
650			_aCalculus of variations. _920282
650			_aDifferential equations. _920283
650			_aFunctional analysis. _920284
650			_aMathematical physics. _920285
650			_aCalculus of Variations and Optimization. _920286
650			_aDifferential Equations. _920287
650			_aFunctional Analysis. _920288
650			_aMathematical Physics. _920289
856			_uhttps://doi.org/10.1007/978-3-319-77637-8
942			_cEBK
999			_c13625 _d13625