Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains by Vitaly VolpertElliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains by Vitaly Volpert

Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in…

byVitaly Volpert

Paperback | April 21, 2013

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The theory of elliptic partial differential equations has developed during about two centuries together with electrostatics, heat and mass diffusion, hydrodynamics and many other applications. It remains one of the most rapidly developing fields of mathematics. The theory of general elliptic problems is presented in the present first volume of the book. A priori estimates, normal solvability and Fredholm property, index, operators with a parameter, nonlinear Fredholm operators are discussed. Particular attention is paid to elliptic problems in unbounded domains which are not yet sufficiently well presented in the existing literature and which require some special approaches. The second volume will be devoted to reaction-diffusion equations. Existence and bifurcations of solutions, travelling waves, spectral properties and other questions are studied in relation with numerous applications in chemical physics, biology and medicine.
Title:Elliptic Partial Differential Equations: Volume 1: Fredholm Theory of Elliptic Problems in…Format:PaperbackDimensions:642 pagesPublished:April 21, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3034803222

ISBN - 13:9783034803229

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Table of 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.

Editorial Reviews

From the reviews:"In the book under review the author concentrates on the Fredholm theory for (mainly linear) boundary value problems in unbounded domains. . Both for a researcher in the field and for a mathematical research library, this is a must-have item." (Niels Jacob, The Mathematical Gazette, Vol. 98 (541), March, 2014)"This very interesting book presents a systematic study of elliptic problems in unbounded domains of Rn. . At the end of the book . the author gives a comprehensive account of the large development of the elliptic theory from its birth in the XVIIIth century up to the present time. . This historical account gives to the reader the full perspective on each topic as well as a complete and up-to-date bibliography. This is certainly an excellent starting point for any kind of further investigation." (Paolo Acquistapace, Mathematical Reviews, Issue 2012 g)"The book is devoted to substantial and systematic presentation of the linear and nonlinear theory of elliptic partial differential equations in unbounded domains. . The presentation of the results is mostly self-contained. Thus, the book can be recommended either for experts in the subject or for beginners." (Sergei V. Rogosin, Zentralblatt MATH, Vol. 1222, 2011)