Partial Differential Equations [Hardcover]

Jürgen Jost (Author)

Book Description

ISBN-10: 0387954287 | ISBN-13: 978-0387954288 | Publication Date: August 12, 2002 | Edition: 1

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. Jürgen Jost is 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 Postmodern Analysis (1998), Compact Riemann Surfaces (1997) and Riemannian Geometry and Geometric Analysis (1995). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998).

Editorial Reviews

Review

From the reviews:

MATHEMATICAL REVIEWS

"..the composition of this book is somewhat classical. Indeed the author covers the main properties of the elliptic, parabolic and hyperbolic equations. But he always adds some interesting extensions or links between these chapters…this textbook is self-contained…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."

"The author covers the main properties of the elliptic parabolic and hyperbolic equations. But he always adds some interesting extensions or links between these chapters. … With an appendix on general results concerning Banach or Hilbert spaces, this textbook is self-contained. … 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." (Alain Brillard, Mathematical Reviews, 2003f)

"Jost’s book … focuses mainly on elliptic PDEs and gives a comprehensive overview of the modern theory of solving such equations. … There are extremely helpful summaries and a handful of exercises at the end of each of the 11 chapters; an appendix covers background functional analysis. … Throughout, Jost achieves an impeccable blend of motivation, orientation and analysis … . 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, Vol. 88 (512), 2004)

From the Back Cover

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 --This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 344 pages
• Publisher: Springer; 1 edition (August 12, 2002)
• Language: English
• ISBN-10: 0387954287
• ISBN-13: 978-0387954288
• Product Dimensions: 9 x 6.8 x 0.8 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #3,210,030 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

9 of 9 people found the following review helpful:

5.0 out of 5 stars Elliptic PDE's done right, June 16, 2007

By 

A. Castro "traca_virtual" (California , USA) - See all my reviews
(REAL NAME)   

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This review is from: Partial Differential Equations (Hardcover)

I'm no specialist in PDE's but I boldly would like to review the present book.
This book is intended(in my personal view) as a in-depth-but-not-pedantic introduction to Elliptic equations (which, if one considers the original title in german "Partielle Differentialgleichungen - Elliptische Gleichungen" makes complete sense).
As any other descent book, it doesn't aim at list down results in a encyclopedic way, but rather tour-guide the reader in the beautiful subject of Elliptic PDE's.

Motivated by Dirichlet's principle, the author introduces variational methods for Elliptic PDE's and a good deal of the regularity program for that class of equations(including non-linear equations). Most of what follows the first chapter, is a successful attempt to generalize to other elliptic equations the techniques useful in the qualitative theory of the Dirichlet problem for the Poisson equation. Some of the methods, as far as I understand them, can be generalized to Schroedinger's equation too.

The interested reader can consult also the book on analysis by Elliot Lieb and the textbook on variational methods by Prof. S. Hildebrandt(and references therein).

3 of 3 people found the following review helpful:

4.0 out of 5 stars A very good choice, February 5, 2008

By 

areader "jguevara7" (Caracas, D.F. Venezuela) - See all my reviews

This review is from: Partial Differential Equations (Graduate Texts in Mathematics) (Hardcover)

This is an excellent book for a PDE course with a strong vias toward
elliptic and parabolic equations. Its lack of information related to hyperbolic equations is its weakest point. However, the author is an
excellent writer and it is pleasure to read this book.