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Unbounded Functionals in the Calculus of Variations
Af: Luciano Carbone, Riccardo De Arcangelis Engelsk Paperback
SPAR
kr 90
Unbounded Functionals in the Calculus of Variations
Af: Luciano Carbone, Riccardo De Arcangelis Engelsk Paperback
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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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.
Produktdetaljer
Sprog: Engelsk
Sider: 408
ISBN-13: 9780367455071
Indbinding: Paperback
Udgave:
ISBN-10: 0367455072
Udg. Dato: 2 dec 2019
Længde: 0mm
Bredde: 234mm
Højde: 156mm
Oplagsdato: 2 dec 2019
Forfatter(e) Luciano Carbone, Riccardo De Arcangelis


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Paperback


Sider 408


Udgave


Længde 0mm


Bredde 234mm


Højde 156mm


Udg. Dato 2 dec 2019


Oplagsdato 2 dec 2019

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