Elliptic Partial Differential Equations of Second Order

Elliptic Partial Differential Equations of Second Order by David Gilbarg, Neil S. Trudinger.

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Bibliographic Details
Main Authors: Gilbarg, David (Author), Trudinger, Neil S. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2001.
Edition:2nd ed. 2001.
Series:Classics in Mathematics,
Springer eBook Collection.
Subjects:
Partial differential equations.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of 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.

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