Functional Analysis and Applied Optimization in Banach Spaces: Applications to N

Description: Functional Analysis and Applied Optimization in Banach Spaces by Fabio Botelho 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Back Cover 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. 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. Review "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 Lovíšek, Mathematical Reviews, August, 2015) Long Description 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." Review Quote "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." (Jn Lovsek, Mathematical Reviews, August, 2015) Feature Introduces the basic concepts of real and functional analysis Contains introductory and advanced concepts in measure and integration Applications will be of interest to applied mathematicians, physicists, and engineers Details ISBN3319382063 Author Fabio Botelho Year 2016 ISBN-10 3319382063 ISBN-13 9783319382067 Format Paperback Publication Date 2016-08-23 Language English Media Book Imprint Springer International Publishing AG Subtitle Applications to Non-Convex Variational Models Place of Publication Cham Country of Publication Switzerland Illustrations 51 Illustrations, color; 6 Illustrations, black and white; XVIII, 560 p. 57 illus., 51 illus. in color. Pages 560 Short Title Functional Analysis and Applied Optimization in Banach Spaces Edited by Gregor von Cieminski Birth 1968 Affiliation Marquette University Position Assistant Professor Qualifications Ph.D. Publisher Springer International Publishing AG Edition Description Softcover reprint of the original 1st ed. 2014 Alternative 9783319060736 DEWEY 515.732 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:100253275;

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