Buy this book
 About this Textbook

This textbook is intended for students who wish to obtain an introduction to the theory of partial di?erential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not o?er a comprehensive overview of the whole ?eld of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding qu tion is how one can ?nd a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for ?nding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original pr lem. Di?erential equations are posed in spaces of functions, and those spaces are of in?nite dimension.
 Reviews

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 selfcontained…Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these secondorder partial differential equations. Teachers will also find in this textbook the basis of an introductory course on secondorder 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 selfcontained. … Because of the nice global presentation, I recommend this book to students and young researchers who need the now classical properties of these secondorder 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 wellorganised, I strongly recommend this book to anyone seeking a stylish, balanced, uptodate survey of this central area of mathematics." (Nick Lord, The Mathematical Gazette, Vol. 88 (512), 2004)
 Table of contents (12 chapters)


Introduction: What Are Partial Differential Equations?
Pages 16

The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order
Pages 730

The Maximum Principle
Pages 3150

Existence Techniques I: Methods Based on the Maximum Principle
Pages 5175

Existence Techniques II: Parabolic Methods. The Heat Equation
Pages 77112

Table of contents (12 chapters)
Bibliographic Information
 Bibliographic Information

 Book Title
 Partial Differential Equations
 Authors

 J. Jost
 Series Title
 Graduate Texts in Mathematics
 Series Volume
 214
 Copyright
 2002
 Publisher
 SpringerVerlag New York
 Copyright Holder
 Springer Science+Business Media New York
 eBook ISBN
 9780387215952
 DOI
 10.1007/b97312
 Series ISSN
 00725285
 Edition Number
 1
 Number of Pages
 XI, 325
 Topics