Monographs in Mathematics

Elliptic Partial Differential Equations

Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains

Authors: Volpert, Vitaly

  • Offers a systematic investigation of general elliptic problems applicable both for bounded and unbounded domains
  • Includes a focus on unbounded domains, which has not been sufficiently presented in the existing literature
  • Gives a mostly self-contained presentation of the results
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  • ISBN 978-3-0346-0536-6
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  • ISBN 978-3-0348-0322-9
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About this book

<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>

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)


Table of contents (11 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0346-0537-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-0346-0536-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-3-0348-0322-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Partial Differential Equations
Book Subtitle
Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains
Authors
Series Title
Monographs in Mathematics
Series Volume
101
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0346-0537-3
DOI
10.1007/978-3-0346-0537-3
Hardcover ISBN
978-3-0346-0536-6
Softcover ISBN
978-3-0348-0322-9
Series ISSN
1017-0480
Edition Number
1
Number of Pages
XVIII, 642
Topics