二次の楕円型偏微分方程式（第２巻　復刊）<br>Elliptic Partial Differential Equations of Second Order (Classics in Mathematics (CIM)) （Reprint of the 2nd ed. Corr. 3rd printing 1998）

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二次の楕円型偏微分方程式（第２巻　復刊）
Elliptic Partial Differential Equations of Second Order (Classics in Mathematics (CIM)) （Reprint of the 2nd ed. Corr. 3rd printing 1998）

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  • 製本 Paperback:紙装版/ペーパーバック版／ページ数 518 p.
  • 商品コード 9783540411604

基本説明

Originally published as volume 224 in the series: Grundlehren der mathematischen Wissenschaften. 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.

Full Description

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

Contents

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.