Elliptic Partial Differential Equations of Second Order

✍ Scribed by David Gilbarg, Neil S. Trudinger (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2001
• Tongue: English
• Leaves: 530
• Series: Classics in Mathematics 224
• Edition: 2
• Category: Library

✦ Synopsis

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 ZealandMathematical 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 etAppliquées,1985

✦ Table of Contents

Front Matter....Pages N1-xiii
Introduction....Pages 1-10
Front Matter....Pages 11-11
Laplace’s Equation....Pages 13-30
The Classical Maximum Principle....Pages 31-50
Poisson’s Equation and the Newtonian Potential....Pages 51-72
Banach and Hilbert Spaces....Pages 73-86
Classical Solutions; the Schauder Approach....Pages 87-143
Sobolev Spaces....Pages 144-176
Generalized Solutions and Regularity....Pages 177-218
Strong Solutions....Pages 219-257
Front Matter....Pages N3-N3
Maximum and Comparison Principles....Pages 259-278
Topological Fixed Point Theorems and Their Application....Pages 279-293
Equations in Two Variables....Pages 294-318
Hölder Estimates for the Gradient....Pages 319-332
Boundary Gradient Estimates....Pages 333-358
Global and Interior Gradient Bounds....Pages 359-387
Equations of Mean Curvature Type....Pages 388-440
Fully Nonlinear Equations....Pages 441-490
Back Matter....Pages 492-523

✦ Subjects

Partial Differential Equations