**Graduate Studies in Mathematics**

Volume: 19;
2010;
749 pp;
Hardcover

MSC: Primary 35;
Secondary 49; 47

Print ISBN: 978-0-8218-4974-3

Product Code: GSM/19.R

List Price: $93.00

Individual Member Price: $74.40

**Electronic ISBN: 978-1-4704-1144-2
Product Code: GSM/19.R.E**

List Price: $93.00

Individual Member Price: $74.40

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#### Supplemental Materials

# Partial Differential Equations: Second Edition

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*Lawrence C. Evans*

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

—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

#### Table of Contents

# Table of Contents

## Partial Differential Equations: Second Edition

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface to the second edition xvii18 free
- Preface to the first edition xix20 free
- Chapter 1. Introduction 124 free
- Chapter 2. Four important linear partial differential equations 1740 free
- Chapter 3. Nonlinear first-order PDE 91114
- Chapter 4. Other ways to represent solutions 167190
- Chapter 5. Sobolev spaces 255278
- Chapter 6. Second-order elliptic equations 313336
- Chapter 7. Linear evolution equations 373396
- Chapter 8. The calculus of variations 455478
- Chapter 9. Nonvariational techniques 529552
- Chapter 10. Hamilton–Jacobi equations 581604
- Chapter 11. Systems of conservation laws 611634
- Chapter 12. Nonlinear wave equations 661684
- Appendix A: Notation 699722
- Appendix B: Inequalities 707730
- Appendix C: Calculus 712735
- Appendix D: Functional Analysis 722745
- Appendix E: Measure Theory 732755
- Bibliography 739762
- Index 745768 free
- Back Cover Back Cover1778

#### Readership

Graduate students and research mathematicians interested in partial differential equations.

#### Reviews

This second edition of the textbook addresses even more of the current research directions on PDEs and Professor Evans should be praised for taking the time and effort to make an already successful and wonderful book even better. Needless to say, I recommend this book, with unreserved enthusiasm, to anyone with an interest on the study of PDEs.

-- Mathematical Reviews

This book would be invaluable for a graduate student preparing to do research in PDEs; I wish I had a copy in graduate school.

-- MAA Reviews