Elliptic Partial Differential Equations of Second Order

Nachdruck of the 2. Auflage Berlin Heidelberg New York 1983. Corr. 3rd printing 1998
ISBN: 978-3-540-41160-4
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 518 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1660 g

Reihe: Classics in Mathematics

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." --New Zealand Mathematical Society, 1985

Zielgruppe

Research

Autoren/Hrsg.

Trudinger, Neil S.

Gilbarg, David

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

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.

Über Autor(innen)

David Gilbarg was born in New York in 1918, and was educated there through udergraduate school. He received his Ph.D. degree at Indiana University in 1941. His work in fluid dynamics during the war years motivated much of his later research on flows with free boundaries. He was on the Mathematics faculty at Indiana University from 1946 to 1957 and at Stanford University from 1957 on. His principal interests and contributions have been in mathematical fluid dynamics and the theory of elliptic partial differential equations.

Neil S. Trudinger was born in Ballarat, Australia in 1942. After schooling and undergraduate education in Australia, he completed his PhD at Stanford University, USA in 1966. He has been a Professor of Mathematics at the Australian National University, Canberra since 1973. His research contributions, while largely focussed on non-linear elliptic partial differential equations, have also spread into geometry, functional analysis and computational mathematics. Among honours received are Fellowships of the Australian Academy of Science and of the Royal Society of London.