Elliptic Equations: An Introductory Course

- Preface

I. 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

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)