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Elliptic Partial Differential Equations [electronic resource] : Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains / by Vitaly Volpert.

By: Volpert, Vitaly [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Monographs in Mathematics: 101Publisher: Basel : Springer Basel, 2011Description: XVIII, 642 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783034605373.Subject(s): Mathematics | Differential equations, partial | Mathematics | Partial Differential EquationsDDC classification: 515.353 Online resources: Click here to access online
Contents:
Chapter 1. Introduction -- Chapter 2. Function spaces and operators -- Chapter 3. A priori estimates -- Chapter 4. Normal solvability -- Chapter 5. Fredholm property -- Chapter 6. Formally adjoint problems -- Chapter 7. Elliptic problems with a parameter -- Chapter 8. Index of elliptic operators -- Chapter 9. Problems in cylinders -- Chapter 10. Non-Fredholm operators -- Chapter 11. Nonlinear Fredholm operators -- Supplement. Discrete operators.-Historical and bibliographical comments -- Acknowledgements -- References.
In: Springer eBooksSummary: <p>The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments.</p> <p>The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.</p>
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Chapter 1. Introduction -- Chapter 2. Function spaces and operators -- Chapter 3. A priori estimates -- Chapter 4. Normal solvability -- Chapter 5. Fredholm property -- Chapter 6. Formally adjoint problems -- Chapter 7. Elliptic problems with a parameter -- Chapter 8. Index of elliptic operators -- Chapter 9. Problems in cylinders -- Chapter 10. Non-Fredholm operators -- Chapter 11. Nonlinear Fredholm operators -- Supplement. Discrete operators.-Historical and bibliographical comments -- Acknowledgements -- References.

The theory of elliptic partial differential equations has undergone an important development over the last two centuries. Together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications, it has become one of the most richly enhanced fields of mathematics. This monograph undertakes a systematic presentation of the theory of general elliptic operators. The author discusses a priori estimates, normal solvability, the Fredholm property, the index of an elliptic operator, operators with a parameter, and nonlinear Fredholm operators. Particular attention is paid to elliptic problems in unbounded domains which have not yet been sufficiently treated in the literature and which require some special approaches. The book also contains an analysis of non-Fredholm operators and discrete operators as well as extensive historical and bibliographical comments.

The selected topics and the author's level of discourse will make this book a most useful resource for researchers and graduate students working in the broad field of partial differential equations and applications.

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