Partial Differential EquationsAmerican Mathematical Soc., 2010 - 749 Seiten This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections, a significantly expanded bibliography. About the First Edition: I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail...Evans' book is evidence of his mastering of the field and the clarity of presentation (Luis Caffarelli, University of Texas) It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ...Every graduate student in analysis should read it. (David Jerison, MIT) I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ...I am very happy with the preparation it provides my students. (Carlos Kenig, University of Chicago) Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ...An outstanding reference for many aspects of the field. (Rafe Mazzeo, Stanford University. |
Inhalt
| 2 | |
| 15 | |
Nonlinear FirstOrder PDE | 91 |
Other Ways to Represent Solutions | 167 |
THEORY FOR LINEAR PARTIAL | 253 |
This chapter surveys the principal theoretical issues concerning the solv | 255 |
ically a typical PDE as follows Fix an integer k 1 and let U denote | 292 |
10 | 295 |
The Calculus of Variations | 455 |
Nonvariational Techniques | 529 |
Nonlinear Wave Equations | 661 |
APPENDICES | 699 |
Inequalities | 707 |
Functional Analysis | 722 |
Measure Theory | 732 |
| 739 | |
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according apply appropriate assertion Assume Banach space boundary bounded calculations called Chapter choose coefficients compact compute condition Consequently conservation consider constant continuous converges convex corresponding deduce define DEFINITION denote depending derivatives eigenvalue elliptic energy equality equation estimate Example exists fact follows formula function Furthermore given Hence holds hyperbolic identity implies inequality initial initial-value problem integral Lemma linear mapping method minimizer nonlinear Observe obtain operator parabolic partial differential equations particular problem Proof prove recall regularity Remark satisfies smooth smooth function smooth solution solves space Suppose term Theorem theory transform unique variables variations wave equation weak solution write