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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Unbounded Functionals in the Calculus of Variations - Representation, Relaxation, and Homogenization (Paperback)
Loot Price: R1,480
Discovery Miles 14 800
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Unbounded Functionals in the Calculus of Variations - Representation, Relaxation, and Homogenization (Paperback)
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Over the last few decades, research in elastic-plastic torsion
theory, electrostatic screening, and rubber-like nonlinear
elastomers has pointed the way to some interesting new classes of
minimum problems for energy functionals of the calculus of
variations. This advanced-level monograph addresses these issues by
developing the framework of a general theory of integral
representation, relaxation, and homogenization for unbounded
functionals. The first part of the book builds the foundation for
the general theory with concepts and tools from convex analysis,
measure theory, and the theory of variational convergences. The
authors then introduce some function spaces and explore some lower
semicontinuity and minimization problems for energy functionals.
Next, they survey some specific aspects the theory of standard
functionals. The second half of the book carefully develops a
theory of unbounded, translation invariant functionals that leads
to results deeper than those already known, including unique
extension properties, representation as integrals of the calculus
of variations, relaxation theory, and homogenization processes. In
this study, some new phenomena are pointed out. The authors'
approach is unified and elegant, the text well written, and the
results intriguing and useful, not just in various fields of
mathematics, but also in a range of applied mathematics, physics,
and material science disciplines.
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