Functional Analysis and Applied Optimization in Banach Spaces Applications to Non-Convex Variational Models /
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...
| Published in: | Springer eBooks |
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| Format: | eBook |
| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2014.
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| Online Access: | http://dx.doi.org/10.1007/978-3-319-06074-3 Перейти в каталог НБ ТГУ |
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 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.