Overview
- New edition extensively revised and updated
- Features a systematic discussion of the relations between different types of partial differential equations
- Presents new Harnack type techniques
Part of the book series: Graduate Texts in Mathematics (GTM, volume 214)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
- Brownian motion
- Harnack inequality
- Hilbert space methods
- Moser iteration
- Schauder estimates
- Sobolev spaces
- Turing mechanism
- eigenvalues
- harmonic functions
- heat equation
- maximum principle
- nonlinear partial differential equations
- pattern formation
- reaction-diffusion equations and systems
- semigroups
- wave equation
- partial differential equations
About this book
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations.
This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.
Reviews
From the book reviews:
“This graduate-level book is an introduction to the modern theory of partial differential equations (PDEs) with an emphasis on elliptic PDEs. … The book is undoubtedly a success in the presentation of diverse methods in PDEs at such an introductory level. The reader has a great opportunity to learn basic techniques underlying current research in elliptic PDEs and be motivated for advanced theory of more general elliptic PDEs and nonlinear PDEs.” (Dhruba Adhikari, MAA Reviews, December, 2014)
“This revised version gives an introduction to the theory of partial differential equations. … Every chapter has at the end a very helpful summary and some exercises. This book is very useful for a PhD course.” (Vincenzo Vespri, Zentralblatt MATH, Vol. 1259, 2013)
"Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these second-order partial differential equations. Teachers will also find in this textbook the basis of an introductory course on second-order partial differential equations."
- Alain Brillard, Mathematical Reviews
"Beautifully written and superbly well-organised, I strongly recommend this book to anyone seeking a stylish, balanced, up-to-date survey of this central area of mathematics."
- Nick Lord, The Mathematical Gazette
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Partial Differential Equations
Authors: Jürgen Jost
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-4809-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2013
Hardcover ISBN: 978-1-4614-4808-2Published: 13 November 2012
Softcover ISBN: 978-1-4939-0247-7Published: 13 December 2014
eBook ISBN: 978-1-4614-4809-9Published: 13 November 2012
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 3
Number of Pages: XIII, 410
Number of Illustrations: 10 b/w illustrations
Topics: Partial Differential Equations, Theoretical, Mathematical and Computational Physics