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The Resource Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models, by Fabio Botelho, (electronic resource)

Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models, by Fabio Botelho, (electronic resource)

Label
Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models
Title
Functional Analysis and Applied Optimization in Banach Spaces
Title remainder
Applications to Non-Convex Variational Models
Statement of responsibility
by Fabio Botelho
Creator
Contributor
Author
Subject
Language
eng
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
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorName
Botelho, Fábio
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink (Online service)
Series statement
Springer eBooks
http://library.link/vocab/subjectName
  • Mathematics
  • Fourier analysis
  • Functional analysis
  • Numerical analysis
Label
Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models, by Fabio Botelho, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-06074-3
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent.
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 Computation in the Ginzburg-Landau System.- 17. On Duality Principles for Scalar and Vectorial Multi-Well Variational Problems -- 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
Control code
978-3-319-06074-3
Dimensions
unknown
Extent
XVIII, 560 pages 57 illustrations, 51 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319060743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
c
Other control number
10.1007/978-3-319-06074-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086513942
Label
Functional Analysis and Applied Optimization in Banach Spaces : Applications to Non-Convex Variational Models, by Fabio Botelho, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-06074-3
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent.
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 Computation in the Ginzburg-Landau System.- 17. On Duality Principles for Scalar and Vectorial Multi-Well Variational Problems -- 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
Control code
978-3-319-06074-3
Dimensions
unknown
Extent
XVIII, 560 pages 57 illustrations, 51 illustrations in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319060743
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
c
Other control number
10.1007/978-3-319-06074-3
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086513942

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