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Hardcover ISBN:  9780821805695 
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Product Code:  GSM/12.B 
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Hardcover ISBN:  9780821805695 
Product Code:  GSM/12 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470420703 
Product Code:  GSM/12.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821805695 
eBook ISBN:  9781470420703 
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 boundaryvalue problems for elliptic and parabolic equations, with some guidelines concerning other boundaryvalue problems such as the Neumann or oblique derivative problems or problems involving higherorder 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. Secondorder elliptic equations in half spaces

Chapter 6. Secondorder elliptic equations in smooth domains

Chapter 7. Elliptic equations in nonsmooth domains

Chapter 8. Parabolic equations in the whole space

Chapter 9. Boundaryvalue 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


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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 boundaryvalue problems for elliptic and parabolic equations, with some guidelines concerning other boundaryvalue problems such as the Neumann or oblique derivative problems or problems involving higherorder 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. Secondorder elliptic equations in half spaces

Chapter 6. Secondorder elliptic equations in smooth domains

Chapter 7. Elliptic equations in nonsmooth domains

Chapter 8. Parabolic equations in the whole space

Chapter 9. Boundaryvalue 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