| Hardcover ISBN: | 978-0-8218-0569-5 |
| Product Code: | GSM/12 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-2070-3 |
| Product Code: | GSM/12.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-0569-5 |
| eBook: ISBN: | 978-1-4704-2070-3 |
| Product Code: | GSM/12.B |
| List Price: | $184.00 $141.50 |
| MAA Member Price: | $165.60 $127.35 |
| AMS Member Price: | $147.20 $113.20 |
| Hardcover ISBN: | 978-0-8218-0569-5 |
| Product Code: | GSM/12 |
| List Price: | $99.00 |
| MAA Member Price: | $89.10 |
| AMS Member Price: | $79.20 |
| eBook ISBN: | 978-1-4704-2070-3 |
| Product Code: | GSM/12.E |
| List Price: | $85.00 |
| MAA Member Price: | $76.50 |
| AMS Member Price: | $68.00 |
| Hardcover ISBN: | 978-0-8218-0569-5 |
| eBook ISBN: | 978-1-4704-2070-3 |
| Product Code: | GSM/12.B |
| List Price: | $184.00 $141.50 |
| MAA Member Price: | $165.60 $127.35 |
| AMS Member Price: | $147.20 $113.20 |
-
Book DetailsGraduate Studies in MathematicsVolume: 12; 1996; 164 ppMSC: Primary 35
This book concentrates on fundamentals of the modern theory of linear elliptic and parabolic equations in Hölder spaces. The author shows that this theory—including some issues of the theory of nonlinear equations—is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed.
With nearly 200 exercises, this book provides a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.
ReadershipGraduate students and researchers in mathematics, physics, and engineering interested in the theory of partial differential equations.
-
Table of Contents
-
Chapters
-
Chapter 1. Elliptic equations with constant coefficients in $\mathbb {R}^d$
-
Chapter 2. Laplace’s equation
-
Chapter 3. Solvability of elliptic equations with constant coefficients in the Hölder spaces
-
Chapter 4. Elliptic equations with variable coefficients in $\mathbb {R}^d$
-
Chapter 5. Second-order elliptic equations in half spaces
-
Chapter 6. Second-order elliptic equations in smooth domains
-
Chapter 7. Elliptic equations in non-smooth domains
-
Chapter 8. Parabolic equations in the whole space
-
Chapter 9. Boundary-value problems for parabolic equations in half spaces
-
Chapter 10. Parabolic equations in domains
-
-
Reviews
-
Short but not condensed, well organized and gives a stimulating presentation of basic aspects of the theory of elliptic and parabolic equations in Hölder spaces ... an interesting addition for students and instructors.
Zentralblatt MATH -
The author has fully achieved his goal ... and has written an impressive book that presents nice material in an interesting way ... this book can be recommended as a thorough, modern and sufficiently broad introduction to partial differential equations of elliptic and parabolic types for graduate students and instructors (and also for individual study) in mathematics, physics, and (possibly) engineering.
Mathematical Reviews
-
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Reviews
- Requests
This book concentrates on fundamentals of the modern theory of linear elliptic and parabolic equations in Hölder spaces. The author shows that this theory—including some issues of the theory of nonlinear equations—is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed.
With nearly 200 exercises, this book provides a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.
Graduate students and researchers in mathematics, physics, and engineering interested in the theory of partial differential equations.
-
Chapters
-
Chapter 1. Elliptic equations with constant coefficients in $\mathbb {R}^d$
-
Chapter 2. Laplace’s equation
-
Chapter 3. Solvability of elliptic equations with constant coefficients in the Hölder spaces
-
Chapter 4. Elliptic equations with variable coefficients in $\mathbb {R}^d$
-
Chapter 5. Second-order elliptic equations in half spaces
-
Chapter 6. Second-order elliptic equations in smooth domains
-
Chapter 7. Elliptic equations in non-smooth domains
-
Chapter 8. Parabolic equations in the whole space
-
Chapter 9. Boundary-value problems for parabolic equations in half spaces
-
Chapter 10. Parabolic equations in domains
-
Short but not condensed, well organized and gives a stimulating presentation of basic aspects of the theory of elliptic and parabolic equations in Hölder spaces ... an interesting addition for students and instructors.
Zentralblatt MATH -
The author has fully achieved his goal ... and has written an impressive book that presents nice material in an interesting way ... this book can be recommended as a thorough, modern and sufficiently broad introduction to partial differential equations of elliptic and parabolic types for graduate students and instructors (and also for individual study) in mathematics, physics, and (possibly) engineering.
Mathematical Reviews
