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  • Textbook
  • © 2013

Partial Differential Equations

Authors:

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  • 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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USD 59.99
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  • ISBN: 978-1-4614-4809-9
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Softcover Book
USD 37.99 USD 74.99
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Hardcover Book
USD 49.99 USD 109.99
55% discount Price excludes VAT (USA)

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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.

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

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

  • für Mathematik in den Naturwissenschafte, Max Planck Institut für Mathematik in den Naturwissenschafte, Leipzig, Germany

    Jürgen Jost

About the author

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.

Bibliographic Information

Buying options

eBook
USD 59.99
Price excludes VAT (USA)
  • ISBN: 978-1-4614-4809-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 37.99 USD 74.99
49% discount Price excludes VAT (USA)
Hardcover Book
USD 49.99 USD 109.99
55% discount Price excludes VAT (USA)