Functional Analysis and Applied Optimization in Banach Spaces

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.

"The aim of the present book is to consider a variety of problems arising in applications in relation with non-convex variational models. ... The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics, and engineering." (Ján Lovísek, Mathematical Reviews, August, 2015)