Overview
- Systematic investigation of general elliptic problems applicable
- both for bounded and unbounded domains
- Focus on unbounded domains which has not been sufficiently presented in the existing literature
- Mostly self-contained presentation of the results
- Includes supplementary material: sn.pub/extras
Part of the book series: Monographs in Mathematics (MMA, volume 101)
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Table of contents (11 chapters)
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Elliptic Partial Differential Equations
Book Subtitle: Volume 1: Fredholm Theory of Elliptic Problems in Unbounded Domains
Authors: Vitaly Volpert
Series Title: Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-0346-0537-3
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel AG 2011
Hardcover ISBN: 978-3-0346-0536-6Published: 06 March 2011
Softcover ISBN: 978-3-0348-0322-9Published: 21 April 2013
eBook ISBN: 978-3-0346-0537-3Published: 03 March 2011
Series ISSN: 1017-0480
Series E-ISSN: 2296-4886
Edition Number: 1
Number of Pages: XVII, 639
Topics: Partial Differential Equations