Functional analysis and applied optimization in Banach spaces : applications to non-convex variational models /

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Bibliographic Details
Author / Creator:	Botelho, Fabio, author.
Imprint:	Cham : Springer, 2014.
Description:	1 online resource (xviii, 560 pages) : illustrations (some color)
Language:	English
Subject:	Functional analysis. Banach spaces. Mathematical optimization. Banach spaces. Functional analysis. Mathematical optimization. Mathematics.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11085878

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ISBN:	9783319060743 3319060740 3319060732 9783319060736
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed June 20, 2014).
Summary:	This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.
Other form:	Printed edition: 9783319060736
Standard no.:	10.1007/978-3-319-06074-3

Table of Contents:

1. Topological Vector Spaces
2. The Hahn-Bananch Theorems and Weak Topologies
3. Topics on Linear Operators
4. Basic Results on Measure and Integration.-5. The Lebesgue Measure in Rn
6. Other Topics in Measure and Integration
7. Distributions
8. The Lebesque and Sobolev Spaces.-9. Basic Concepts on the Calculus of Variations
10. Basic Concepts on Convex Analysis
11. Constrained Variational Analysis
12. Duality Applied to Elasticity
13. Duality Applied to a Plate Model
14. About Ginzburg-Landau Type Equations: The Simpler Real Case.-15. Full Complex Ginzburg-Landau System.-16. More on Duality and Computationin theGinzburg-Landau System.- 17. On Duality Principles for Scalar and Vectorial Multi-Well VariationalProblems
18. More on Duality Principles for Multi-Well Problems
19. Duality and Computation for Quantum Mechanics Models
20. Duality Applied to the Optimal Design in Elasticity
21. Duality Applied to Micro-magnetism
22. The Generalized Method of Lines Applied to Fluid Mechanics
23. Duality Applied to the Optimal Control and Optimal Design of a Beam Model.

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