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This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem.
The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space.
There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem.
The main purpose of the book is to provide a tool for graduate and postgraduate students interested in partial differential equations, as well as a useful reference for researchers active in the field. Prerequisites include a knowledge of classical analysis, differential calculus, Banach and Hilbert spaces, integration and the related standard functional spaces, as well as the Fourier transformation on the Schwartz space.
There are complete and detailed proofs of almost all the results announced and, in some cases, more than one proof is provided in order to highlight different features of the result. Each chapter concludes with a range of exercises of varying levels of difficulty, with hints to solutions provided for many of them.
Complements Adams' Sobolev Spaces in comprising a complete presentation of functional spaces but combined with abstract convex analysis
Gathers together results from functional analysis that make it easier to understand the nature and properties of the functions occurring in these equations, as well as the constraints they must obey to qualify as solutions
Provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing
Includes supplementary material: [...]
Preliminaries on ellipticity.- Notions from Topology and Functional Analysis.- Sobolev Spaces and Embedding Theorems.- Traces of Functions on Sobolev Spaces.- Fractional Sobolev Spaces.- Elliptic PDE: Variational Techniques.- Distributions with measures as derivatives.- Korn's Inequality in Lp.- Appendix on Regularity.
Erscheinungsjahr: | 2012 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 488 |
Reihe: | Universitext |
Inhalt: |
xviii
465 S. 11 s/w Illustr. 465 p. 11 illus. |
ISBN-13: | 9781447128069 |
ISBN-10: | 1447128060 |
Sprache: | Englisch |
Herstellernummer: | 80134373 |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Demengel, Françoise
Demengel, Gilbert |
Übersetzung: | Erné, Reinie |
Auflage: | 2012 |
Hersteller: |
Springer London
Universitext |
Maße: | 235 x 155 x 27 mm |
Von/Mit: | Françoise Demengel (u. a.) |
Erscheinungsdatum: | 23.01.2012 |
Gewicht: | 0,733 kg |
Complements Adams' Sobolev Spaces in comprising a complete presentation of functional spaces but combined with abstract convex analysis
Gathers together results from functional analysis that make it easier to understand the nature and properties of the functions occurring in these equations, as well as the constraints they must obey to qualify as solutions
Provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing
Includes supplementary material: [...]
Preliminaries on ellipticity.- Notions from Topology and Functional Analysis.- Sobolev Spaces and Embedding Theorems.- Traces of Functions on Sobolev Spaces.- Fractional Sobolev Spaces.- Elliptic PDE: Variational Techniques.- Distributions with measures as derivatives.- Korn's Inequality in Lp.- Appendix on Regularity.
Erscheinungsjahr: | 2012 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Taschenbuch |
Seiten: | 488 |
Reihe: | Universitext |
Inhalt: |
xviii
465 S. 11 s/w Illustr. 465 p. 11 illus. |
ISBN-13: | 9781447128069 |
ISBN-10: | 1447128060 |
Sprache: | Englisch |
Herstellernummer: | 80134373 |
Ausstattung / Beilage: | Paperback |
Einband: | Kartoniert / Broschiert |
Autor: |
Demengel, Françoise
Demengel, Gilbert |
Übersetzung: | Erné, Reinie |
Auflage: | 2012 |
Hersteller: |
Springer London
Universitext |
Maße: | 235 x 155 x 27 mm |
Von/Mit: | Françoise Demengel (u. a.) |
Erscheinungsdatum: | 23.01.2012 |
Gewicht: | 0,733 kg |