From the reviews:
"This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985
" . . . as should be clear from the previous discussion, this book is a bibliographical monument to the theory of both theoretical and applied PDEs that has not acquired any flaws due to its age. On the contrary, it remains a crucial and essential tool for the active research in the field. In a few words, in my modest opinion, ". . . this book contains the essential background that a researcher in elliptic PDEs should possess the day s/he gets a permanent academic position. . . ." SIAM Newsletter
Inhaltsverzeichnis
1. Introduction. - I. Linear Equations. - 2. Laplace s Equation. - 3. The Classical Maximum Principle. - 4. Poisson s Equation and the Newtonian Potential. - 5. Banach and Hubert Spaces. - 6. Classical Solutions; the Schauder Approach. - 7. Sobolev Spaces. - 8. Generalized Solutions and Regularity. - 9. Strong Solutions. - II. Quasilinear Equations. - 10. Maximum and Comparison Principles. - 11. Topological Fixed Point Theorems and Their Application. - 12. Equations in Two Variables. - 13. Hölder Estimates for the Gradient. - 14. Boundary Gradient Estimates. - 15. Global and Interior Gradient Bounds. - 16. Equations of Mean Curvature Type. - 17. Fully Nonlinear Equations. - Epilogue. - Notation Index.
