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Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - Ziemer, William P.
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Ziemer, William P.:

Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - edition reliée, livre de poche

1989, ISBN: 9780387970172

Springer, Gebundene Ausgabe, Auflage: 1989, 324 Seiten, Publiziert: 1989-09-18T00:00:01Z, Produktgruppe: Buch, 1.42 kg, Verkaufsrang: 2374564, Mathematik, Naturwissenschaften & Technik, K… Plus…

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Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - Ziemer, William P.
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Ziemer, William P.:

Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - edition reliée, livre de poche

1989, ISBN: 9780387970172

Springer, Gebundene Ausgabe, Auflage: 1989, 324 Seiten, Publiziert: 1989-09-18T00:00:01Z, Produktgruppe: Buch, 3.13 kg, Verkaufsrang: 2377726, Mathematik, Naturwissenschaften & Technik, K… Plus…

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Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - Ziemer, William P.
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Ziemer, William P.:
Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - edition reliée, livre de poche

1989

ISBN: 9780387970172

Springer, Gebundene Ausgabe, Auflage: 1989, 324 Seiten, Publiziert: 1989-09-18T00:00:01Z, Produktgruppe: Buch, 1.42 kg, Verkaufsrang: 2349465, Mathematik, Naturwissenschaften & Technik, K… Plus…

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Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - Ziemer, William P.
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Ziemer, William P.:
Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120) - edition reliée, livre de poche

1989, ISBN: 9780387970172

Springer, Gebundene Ausgabe, Auflage: 1989, 324 Seiten, Publiziert: 1989-09-18T00:00:01Z, Produktgruppe: Buch, 3.13 kg, Verkaufsrang: 2292271, Mathematik, Naturwissenschaften & Technik, K… Plus…

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William P. Ziemer:
Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics) - edition reliée, livre de poche

1989, ISBN: 9780387970172

Springer, 1989-09-18. Hardcover. Good., Springer, 1989-09-18, 2.5

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Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120)
Auteur:
Titre:
ISBN:

9780387970172


The major thrust of this book is the analysis of pointwise behavior of Sobolev functions of integer order and BV functions (functions whose partial derivatives are measures with finite total variation). The development of Sobolev functions includes an analysis of their continuity properties in terms of Lebesgue points, approximate continuity, and fine continuity as well as a discussion of their higher order regularity properties in terms of Lp-derivatives. This provides the foundation for further results such as a strong approximation theorem and the comparison of Lp and distributional derivatives. Also included is a treatment of Sobolev-Poincaré type inequalities which unifies virtually all inequalities of this type. Although the techniques required for the discussion of BV functions are completely different from those required for Sobolev functions, there are similarities between their developments such as a unifying treatment of Poincaré-type inequalities for BV functions. This book is intended for graduate students and researchers whose interests may include aspects of approximation theory, the calculus of variations, partial differential equations, potential theory and related areas. The only prerequisite is a standard graduate course in real analysis since almost all of the material is accessible through real variable techniques.

Informations détaillées sur le livre - Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation (Graduate Texts in Mathematics, 120, Band 120)


EAN (ISBN-13): 9780387970172
ISBN (ISBN-10): 0387970177
Version reliée
Livre de poche
Date de parution: 2007
Editeur: Springer
330 Pages
Poids: 0,660 kg
Langue: eng/Englisch

Livre dans la base de données depuis 2007-03-19T17:12:01+01:00 (Zurich)
Page de détail modifiée en dernier sur 2023-12-25T17:22:40+01:00 (Zurich)
ISBN/EAN: 9780387970172

ISBN - Autres types d'écriture:
0-387-97017-7, 978-0-387-97017-2
Autres types d'écriture et termes associés:
Auteur du livre: sobolev, william ziemer
Titre du livre: sobolev spaces, weakly differentiable functions, function spaces, sobolev space, graduate texts mathematics

Données de l'éditeur

Auteur: William P. Ziemer
Titre: Graduate Texts in Mathematics; Weakly Differentiable Functions - Sobolev Spaces and Functions of Bounded Variation
Editeur: Springer; Springer US
308 Pages
Date de parution: 1989-09-18
New York; NY; US
Langue: Anglais
90,94 € (DE)
93,49 € (AT)
100,50 CHF (CH)
Available
XVI, 308 p.

BB; Hardcover, Softcover / Mathematik/Analysis; Mathematische Analysis, allgemein; Verstehen; Derivative; Potential theory; calculus; compactness; differential equation; Potential Theory; BC

1 Preliminaries.- 1.1 Notation.- 1.2 Measures on Rn.- 1.3 Covering Theorems.- 1.4 Hausdorff Measure.- 1.5 Lp-Spaces.- 1.6 Regularization.- 1.7 Distributions.- 1.8 Lorentz Spaces.- Exercises.- Historical Notes.- 2 Sobolev Spaces and Their Basic Properties.- 2.1 Weak Derivatives.- 2.2 Change of Variables for Sobolev Functions.- 2.3 Approximation of Sobolev Functions by Smooth Functions.- 2.4 Sobolev Inequalities.- 2.5 The Rellich-Kondrachov Compactness Theorem.- 2.6 Bessel Potentials and Capacity.- 2.7 The Best Constant in the Sobolev Inequality.- 2.8 Alternate Proofs of the Fundamental Inequalities.- 2.9 Limiting Cases of the Sobolev Inequality.- 2.10 Lorentz Spaces, A Slight Improvement.- Exercises.- Historical Notes.- 3 Pointwise Behavior of Sobolev Functions.- 3.1 Limits of Integral Averages of Sobolev Functions.- 3.2 Densities of Measures.- 3.3 Lebesgue Points for Sobolev Functions.- 3.4 LP-Derivatives for Sobolev Functions.- 3.5 Properties of Lp-Derivatives.- 3.6 An Lp-Version of the Whitney Extension Theorem.- 3.7 An Observation on Differentiation.- 3.8 Rademacher’s Theorem in the Lp-Context.- 3.9 The Implications of Pointwise Differentiability.- 3.10 A Lusin-Type Approximation for Sobolev Functions.- 3.11 The Main Approximation.- Exercises.- Historical Notes.- 4 Poincaré Inequalities—A Unified Approach.- 4.1 Inequalities in a General Setting.- 4.2 Applications to Sobolev Spaces.- 4.3 The Dual of WM,p(?).- 4.4 Some Measures in (W0M,p(?))*.- 4.5 Poincaré Inequalities.- 4.6 Another Version of Poincaré’s Inequality.- 4.7 More Measures in (WM,p(?))*.- 4.8 Other Inequalities Involving Measures in (WM,p)*.- 4.9 The Case p= 1.- Exercises.- Historical Notes.- 5 Functions of Bounded Variation.- 5.1 Definitions.- 5.2 Elementary Properties of BV Functions.- 5.3Regularization of BV Functions.- 5.4 Sets of Finite Perimeter.- 5.5 The Generalized Exterior Normal.- 5.6 Tangential Properties of the Reduced Boundary and the Measure-Theoretic Normal.- 5.7 Rectifiability of the Reduced Boundary.- 5.8 The Gauss-Green Theorem.- 5.9 Pointwise Behavior of BV Functions.- 5.10 The Trace of a BV Function.- 5.11 Sobolev-Type Inequalities for BV Functions.- 5.12 Inequalities Involving Capacity.- 5.13 Generalizations to the Case p> 1.- 5.14 Trace Defined in Terms of Integral Averages.- Exercises.- Historical Notes.- List of Symbols.
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