Partial Differential EquationsAmerican Mathematical Soc., 2010 - 749 páginas 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. |
Índice
Nonlinear FirstOrder PDE 3 1 Complete integrals envelopes | 91 |
Other Ways to Represent Solutions | 167 |
THEORY FOR LINEAR PARTIAL | 253 |
REPRESENTATION FORMULAS | 255 |
12 | 277 |
ically a typical PDE as follows Fix an integer k 1 and let U denote | 281 |
SecondOrder Elliptic Equations | 313 |
Linear Evolution Equations | 373 |
HamiltonJacobi Equations | 581 |
Systems of Conservation Laws | 611 |
Nonlinear Wave Equations | 661 |
APPENDICES | 699 |
Inequalities | 707 |
Functional Analysis | 722 |
Measure Theory | 732 |
| 739 | |
The Calculus of Variations | 455 |
FOR SOLUTIONS | 486 |
Nonvariational Techniques | 529 |
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Términos y frases comunes
a¹³ assertion Assume boundary conditions boundary-value problem bounded calculate Chapter choose coefficients compact support compute Consequently constant C depending converges convex deduce defined DEFINITION denotes derivatives Du(x Du² dxdt eigenvalues elliptic estimate Euler-Lagrange equation Example exists a constant first-order Fourier transform Furthermore Hamilton-Jacobi equation heat equation Hence hyperbolic identity implies inequality initial-value problem integral L²(U Lagrangian Lemma linear Lipschitz continuous mapping maximum principle minimizer nonlinear NOTATION open set operator parabolic partial differential equations point xo proof of Theorem prove recall satisfies second-order semigroup smooth function smooth solution Sobolev spaces solves Suppose theory unique variables wave equation weak solution weakly write zero ди
