Logo - springer
Slogan - springer

Mathematics - Dynamical Systems & Differential Equations | Partial Differential Equations

Partial Differential Equations

Series: Graduate Texts in Mathematics, Vol. 214

Jost, Jürgen

3rd ed. 2013, XIV, 410 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$59.99

(net) price for USA

ISBN 978-1-4614-4809-9

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$79.95

(net) price for USA

ISBN 978-1-4614-4808-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$79.95

(net) price for USA

ISBN 978-1-4939-0247-7

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • 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

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.

Content Level » Graduate

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

Related subjects » Dynamical Systems & Differential Equations - Theoretical, Mathematical & Computational Physics

Table of contents 

Preface.- Introduction: What are Partial Differential Equations?.- 1 The Laplace equation as the Prototype of an Elliptic Partial Differential Equation of Second Order.- 2 The Maximum Principle.- 3 Existence Techniques I: Methods Based on the Maximum Principle.- 4 Existence Techniques II: Parabolic Methods. The Heat Equation.- 5 Reaction-Diffusion Equations and Systems.- 6 Hyperbolic Equations.- 7 The Heat Equation, Semigroups, and Brownian Motion.- 8 Relationships between Different Partial Differential Equations.- 9 The Dirichlet Principle. Variational Methods for the Solutions of PDEs (Existence Techniques III).- 10 Sobolev Spaces and L^2 Regularity theory.- 11 Strong solutions.- 12 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV).- 13The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash.- Appendix: Banach and Hilbert spaces. The L^p-Spaces.- References.- Index of Notation.- Index.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Partial Differential Equations.