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Calculus of Variations (Paperback, 1st ed. 2018)
Loot Price: R3,804
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Calculus of Variations (Paperback, 1st ed. 2018)
Series: Universitext
Expected to ship within 10 - 15 working days
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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 -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.
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