Elliptic Partial Differential Equations of Second Order [Paperback]

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

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 Math?matiques Pures et Appliqu?es,1985
Chapter 1. Introduction Part I: Linear EquationsChapter 2. Laplace's Equation2.1 The Mean Value Inequalities2.2 Maximum and Minimum Principle2.3 The Harnack Inequality2.4 Green's Representation2.5 The Poisson Integral2.6 Convergence Theorems2.7 Interior Estimates of Derivatives2.8 The Dirichlet Problem; the Method of Subharmonic Functions2.9 CapacityProblemsChapter 3. The Classical Maximum Principle3.1 The Weak Maximum Principle3.2 The Strong Maximum Principle3.3 Apriori Bounds3.4 Gradient Estimates for Poisson's Equation3.5 A Harnack Inequality3.6 Operators in Divergence FormNotesProblemsChapter 4. Poisson's Equation and Newtonian Potential4.1 H?lder Continuity4.2 The Dirichlet Problem for Poisson's Equation4.3 H?lder Estimates for the Second Derivatives4.4 Estimates at the Boundary4.5 H?lder Estimates for the First DerivativesNotesProblemsChapter 5. Banach alƒ-