Unbounded Functionals in the Calculus of Variations
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A01=Luciano Carbone
A01=Riccardo De Arcangelis
advanced energy functional theory
Author_Luciano Carbone
Author_Riccardo De Arcangelis
Banach Space
Basic Function Spaces
Borel
Borel Positive Measure
BV Function
BV Loc
BV Space
calculus of variations
Category=PB
Category=PBKF
Category=PBKJ
Category=PHU
Compact Closure
Convex
Convex Functionals
convex optimization
Convexity Hypotheses
Countability Axiom
Countably Compact
elastic-plastic torsion theory
electrostatic screening
Energy Functionals
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eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
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Finite Positive Measure
functional minimization
Inf
Integral Representation Problems
Lavrentiev Phenomenon
Lim
Lim Inf
Locally
Locally Convex Topological Vector Space
Lower
Lower Semicontinuity
Lower Semicontinuity Properties
mathematical modeling physics
Measure
measure theory applications
Positive
Relaxed Functional
rubber-like nonlinear elastomers
Semicontinuity
Semicontinuous Envelope
Sequentially Compact
Sobolev spaces
Spaces
Topological Vector Space
Translation Invariant
unbounded functionals
Uniform Convergence Topology
variational analysis
Product details
- ISBN 9780367455071
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 02 Dec 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: 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.
Carbone, Luciano; De Arcangelis, Riccardo
