Authors:
- Provides a complete and thorough introduction into the theory of linear and nonlinear partial differential equations
- Presents interesting applications to physics and differential geometry
- Includes the basic methods from linear and nonlinear functional analysis
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
About this book
This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables.
In this first volume, special emphasis is placed on geometric and complex variable methods involving integral representations. The following topics are treated:
• integration and differentiation on manifolds
• foundations of functional analysis
• Brouwer's mapping degree
• generalized analytic functions
• potential theory and spherical harmonics
• linear partial differential equations
This new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added.
The second volume will present functional analytic methods and applications to problems in differential geometry.
This textbook will be of particular use to graduate and postgraduate students interested in this field and will be of interest to advanced undergraduate students. It may also be used for independent study.
Reviews
From the reviews of the second edition:
“The revised and enlarged version of this volume gives a special emphasis to geometric and complex variable methods involving integral representations. The new second edition of this volume has been thoroughly revised and a new section on the boundary behavior of Cauchy’s integral has been added. … This unique book will become a standard reference and it should be found in every mathematical library.” (Vicenţiu D. Rădulescu, Zentralblatt MATH, Vol. 1246, 2012)
Authors and Affiliations
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Mathematical Institute, LS Analysis, Brandenburgian Technical University, Cottbus, Germany
Friedrich Sauvigny
Bibliographic Information
Book Title: Partial Differential Equations 1
Book Subtitle: Foundations and Integral Representations
Authors: Friedrich Sauvigny
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-2981-3
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London 2012
Softcover ISBN: 978-1-4471-2980-6Published: 30 March 2012
eBook ISBN: 978-1-4471-2981-3Published: 28 March 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 2
Number of Pages: XV, 447
Number of Illustrations: 16 b/w illustrations
Topics: Partial Differential Equations, Mathematical Methods in Physics