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Graduate Texts in Mathematics

Partial Differential Equations

Authors: Jost, J.

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  • Presents a modern and systematic treatment of main approaches
  • Several additions have been made to this second edition, including a new chapter on Reaction-diffusion equations
  • Emphasizes methods relevant for both linear and nonlinear equations
  • Contains chapter summaries, detailed illustrations and numerous exercises
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  • ISBN 978-0-387-49319-0
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Softcover $74.99
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  • ISBN 978-1-4419-2380-6
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About this Textbook

This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations.

For the new edition the author has added a new chapter on reaction-diffusion equations and systems. There is also new material on Neumann boundary value problems, Poincaré inequalities, expansions, as well as a new proof of the Hölder regularity of solutions of the Poisson equation.

Jürgen Jost is Co-Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Dynamical Systems (2005), Postmodern Analysis (3rd ed. 2005, also translated into Japanese), Compact Riemann Surfaces (3rd ed. 2006) and Riemannian Geometry and Geometric Analysis (4th ed., 2005). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998).

 

About the first edition:

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

Reviews

From the reviews of the second edition:

"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

“It is an expanded translation by the author of the German original. … The range of methods is wide, covering integral kernels, maximum principles, variational principles, gradient descents, weak derivatives and Sobolev spaces. … the proof are clear and pleasant, provided the reader has a good command in integration theory. … This book is an interesting introduction to the multiple facets of partial differential equations –– especially to regularity theory –– for the reader who has already a good background in analysis.” (Jean Van Schaftingen, Bulletin of the Belgian Mathematical Society, 2007)


Table of contents (13 chapters)

Table of contents (13 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-0-387-49319-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-1-4419-2380-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Partial Differential Equations
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
214
Copyright
2007
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-0-387-49319-0
DOI
10.1007/978-0-387-49319-0
Softcover ISBN
978-1-4419-2380-6
Series ISSN
0072-5285
Edition Number
2
Number of Pages
XIV, 356
Number of Illustrations
10 b/w illustrations
Topics

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