Elliptic Partial Differential Equations of Second Order

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Springer, Mar 30, 2015 - Mathematics - 518 pages
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
"Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985
 

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Contents

Introduction
1
Laplaces Equation
13
The Classical Maximum Principle
31
Poissons Equation and the Newtonian Potential
51
Banach and Hilbert Spaces
73
Classical Solutions the Schauder Approach
87
Sobolev Spaces
144
Generalized Solutions and Regularity
177
Equations in Two Variables
294
Hölder Estimates for the Gradient
319
Boundary Gradient Estimates
333
Global and Interior Gradient Bounds
359
Equations of Mean Curvature Type
388
Fully Nonlinear Equations
441
Bibliography
491
Epilogue
507

Strong Solutions
219
Maximum and Comparison Principles 259
260
Topological Fixed Point Theorems and Their Application
279

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About the author (2015)

Biography of David Gilbarg

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.

Biography of Neil S. Trudinger

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.

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