Synopsis
After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Pablo Pedregal received his Ph.D. degree in Mathematics from the University of Minnesota at the end of 1989, under the guidance of D. Kinderlehrer. Soon after that, he became Associate Professor at U. Complutense. During the academic year 1994-95 he moved to U. de Castilla-La Mancha where he led the Math Department for several years. In 1997 he became full professor. His field of interest focuses on variational techniques applied to optimization in a broad sense, including, but not limited to, calculus of variations--especially vector, non-convex problems--, optimal design in continuous media, optimal control, etc, and more recently he has explored variational ideas in areas like inverse problems, and dynamical systems, as well as optimal control problems governed by hyper-elasticity. He has regularly traveled to research centers in the USA and Europe. He has written more than one hundred research articles, seven specialized books (at least three of them with Springer), and some other of a more didactic style for undergraduates.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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Functional Analysis, Sobolev Spaces, and Calculus of Variations (eng)
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Functional Analysis, Sobolev Spaces, and Calculus of Variations (UNITEXT, 157)
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Functional Analysis, Sobolev Spaces, and Calculus of Variations (UNITEXT, 157)
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Functional Analysis, Sobolev Spaces, and Calculus of Variations (UNITEXT, 157)
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
Edité par
Springer, Berlin, Springer Nature Switzerland, Springer, 2024
ISBN 10 : 3031492455
ISBN 13 : 9783031492457
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations.In this setting, problems become much more involved and,forthis same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the moderncalculus of variationsand the analytical foundation associated with it.Inparticular, it covers an extended introduction to basicfunctional analysisand to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the needforfurther challenges beyond the topicsaddressedhere will push students to more advanced horizons. 387 pp. Englisch. N° de réf. du vendeur 9783031492457
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
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Springer Nature Switzerland, 2024
ISBN 10 : 3031492455
ISBN 13 : 9783031492457
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Covers, in a single source, the full road to treat standard variational problems in solid analytical foundationThe style facilitates progressive understanding, while the set of solved exercises helps in maturing conceptsReference text for a. N° de réf. du vendeur 1199164705
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
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Springer, Springer Jan 2024, 2024
ISBN 10 : 3031492455
ISBN 13 : 9783031492457
Neuf
Taschenbuch
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations. In this setting, problems become much more involved and, for this same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the modern calculus of variations and the analytical foundation associated with it. In particular, it covers an extended introduction to basic functional analysis and to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the need for further challenges beyond the topics addressed here will push students to more advanced horizons.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 404 pp. Englisch. N° de réf. du vendeur 9783031492457
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
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Taschenbuch. Etat : Neu. Functional Analysis, Sobolev Spaces, and Calculus of Variations | Pablo Pedregal | Taschenbuch | UNITEXT | xiv | Englisch | 2024 | Springer | EAN 9783031492457 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. N° de réf. du vendeur 127901471
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Functional Analysis, Sobolev Spaces, and Calculus of Variations
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This book aims at introducing students into the modern analytical foundations to treat problems and situations in the Calculus of Variations solidly and rigorously. Since no background is taken for granted or assumed, as the textbook pretends to be self-contained, areas like basic Functional Analysis and Sobolev spaces are studied to the point that chapters devoted to these topics can be utilized by themselves as an introduction to these important parts of Analysis. The material in this regard has been selected to serve the needs of classical variational problems, leaving broader treatments for more advanced and specialized courses in those areas. It should not be forgotten that problems in the Calculus of Variations historically played a crucial role in pushing Functional Analysis as a discipline on its own right. The style is intentionally didactic. After a first general chapter to place optimization problems in infinite-dimensional spaces in perspective, the first part of the book focuses on the initial important concepts in Functional Analysis and introduces Sobolev spaces in dimension one as a preliminary, simpler case (much in the same way as in the successful book of H. Brezis). Once the analytical framework is covered, one-dimensional variational problems are examined in detail including numerous examples and exercises. The second part dwells, again as a first-round, on another important chapter of Functional Analysis that students should be exposed to, and that eventually will find some applications in subsequent chapters. The first chapter of this part examines continuous operators and the important principles associated with mappings between functional spaces; and another one focuses on compact operators and their fundamental and remarkable properties for Analysis. Finally, the third part advances to multi-dimensional Sobolev spaces and the corresponding problems in the Calculus of Variations.In this setting, problems become much more involved and,forthis same reason, much more interesting and appealing. In particular, the final chapter dives into a number of advanced topics, some of which reflect a personal taste. Other possibilities stressing other kinds of problems are possible. In summary, the text pretends to help students with their first exposure to the moderncalculus of variationsand the analytical foundation associated with it.Inparticular, it covers an extended introduction to basicfunctional analysisand to Sobolev spaces. The tone of the text and the set of proposed exercises will facilitate progressive understanding until the needforfurther challenges beyond the topicsaddressedhere will push students to more advanced horizons. N° de réf. du vendeur 9783031492457
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