Elliptic Equations: An Introductory Course
(Sprache: Englisch)
Avoiding technicalities and refinements, this book introduces different topics in the theory of elliptic partial differential equations. Coverage includes singular perturbation problems, regularity theory, Navier-Stokes system, p-Laplace equation.
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Produktinformationen zu „Elliptic Equations: An Introductory Course “
Avoiding technicalities and refinements, this book introduces different topics in the theory of elliptic partial differential equations. Coverage includes singular perturbation problems, regularity theory, Navier-Stokes system, p-Laplace equation.
Klappentext zu „Elliptic Equations: An Introductory Course “
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues.
The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.
Inhaltsverzeichnis zu „Elliptic Equations: An Introductory Course “
- PrefaceI. Basic techniques
1. Hilbert space techniques
2. A survey of essential analysis
3. Weak formulation of elliptic problems
4. Elliptic problems in divergence form
5. Singular perturbation problems
6. Problems in large cylinders
7. Periodic problems
8. Homogenization
9. Eigenvalues
10. Numerical computations
II. More advanced theory
11. Nonlinear problems
12. L(infinity)-estimates
13. Linear elliptic systems
14. The stationary Navier-Stokes system
15. Some more spaces
16. Regularity theory
17. The p-Laplace equation
18. The strong maximum principle
19. Problems in the whole space
- A. Fixed point theorems
- Bibliography
- Index
Bibliographische Angaben
- Autor: Michel Chipot
- 2009, 290 Seiten, Maße: 17,5 x 25 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3764399813
- ISBN-13: 9783764399818
- Erscheinungsdatum: 19.02.2009
Sprache:
Englisch
Rezension zu „Elliptic Equations: An Introductory Course “
From the reviews:"The present book is devoted to recent advanced results and methods in the theory of linear and nonlinear elliptic equations and systems. ... It is written with great care and is accessible to a large audience including graduate and postgraduate students and researchers in the field of partial differential equations. ... In conclusion, the reviewer may recommend the book as a very good reference for those seeking, new, modern, and powerful techniques in the modern approach of nonlinear elliptic partial differential equations." (Vicentiu D. Radulescu, Zentralblatt MATH, Vol. 1171, 2009)
"The book introduces the reader to a broad spectrum of topics in the theory of elliptic partial differential equations in a simple and systematic way. It provides a comprehensive introductory course to the theory, each chapter being supplemented with interesting exercises for the reader. ... The way of presentation of the material ... keep the reader's attention on the beauty and variety of the issues. ... a very valuable position in the field of elliptic partial differential equations." (Irena Pawlow, Control and Cybernetics, Vol. 39 (3), 2010)
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