Graduate Texts in Mathematics

Partial Differential Equations

Authors: Jost, Jürgen

  • 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
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  • ISBN 978-1-4614-4809-9
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Hardcover $79.95
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  • ISBN 978-1-4614-4808-2
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Softcover $79.95
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  • ISBN 978-1-4939-0247-7
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Rent the ebook  
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About this Textbook

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.

About the authors

Jürgen Jost is currently a codirector of the Max Planck Institute for Mathematics in the Sciences and an honorary professor of mathematics at the University of Leipzig.

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


Table of contents (14 chapters)

  • Introduction: What Are Partial Differential Equations?

    Jost, Jürgen

    Pages 1-7

  • The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order

    Jost, Jürgen

    Pages 9-35

  • The Maximum Principle

    Jost, Jürgen

    Pages 37-57

  • Existence Techniques I: Methods Based on the Maximum Principle

    Jost, Jürgen

    Pages 59-83

  • Existence Techniques II: Parabolic Methods. The Heat Equation

    Jost, Jürgen

    Pages 85-126

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4614-4809-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-1-4614-4808-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4939-0247-7
  • 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
Partial Differential Equations
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
214
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media LLC
eBook ISBN
978-1-4614-4809-9
DOI
10.1007/978-1-4614-4809-9
Hardcover ISBN
978-1-4614-4808-2
Softcover ISBN
978-1-4939-0247-7
Series ISSN
0072-5285
Edition Number
3
Number of Pages
XIII, 410
Number of Illustrations and Tables
10 b/w illustrations
Topics