Elliptic Partial Differential Equations of Second Order

ISBN-10: 3540411607

ISBN-13: 9783540411604

Edition: 2nd 2001 (Reprint)

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Description: 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 Mathmatiques Pures etAppliques,1985

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Book details

List price: $69.99
Edition: 2nd
Copyright year: 2001
Publisher: Springer
Publication date: 1/12/2001
Binding: Paperback
Pages: 518
Size: 6.25" wide x 9.25" long x 1.25" tall
Weight: 1.738
Language: English

Introduction
Linear Equations
Laplace''s Equation
The Mean Value Inequalities
Maximum and Minimum Principle
The Harnack Inequality
Green''s Representation
The Poisson Integral
Convergence Theorems
Interior Estimates of Derivatives
The Dirichlet Problem; the Method of Subharmonic Functions
CapacityProblems
The Classical Maximum Principle
The Weak Maximum Principle
The Strong Maximum Principle
Apriori Bounds
Gradient Estimates for Poisson''s Equation
A Harnack Inequality
Operators in Divergence FormNotesProblems
Poisson''s Equation and Newtonian Potential
H+�lder Continuity
The Dirichlet Problem for Poisson''s Equation
H+�lder Estimates for the Second Derivatives
Estimates at the Boundary
H+�lder Estimates for the First DerivativesNotes Problems
Banach and Hilbert Spaces
The Contraction Mapping
The Method of Cintinuity
The Fredholm Alternative
Dual Spaces and Adjoints
Hilbert Spaces
The Projection Theorem
The Riesz Representation Theorem
The Lax-Milgram Theorem
The Fredholm Alternative in Hilbert Spaces
Weak CompactnessNotesProblems
Classical Solutions; the Schauder Approach
The Schauder Interior Estimates
Boundary and Global Estimates
The Dirichlet Problem
Interior and Boundary Regularity
An Alternative Approach
Non-Uniformly Elliptic Equations
Other Boundary Conditions; the Obliue Derivative Problem
Appendix 1: Interpolation Inequalities
Appendix 2: Extension LemmasNotesProblems
Sobolev Spaces
L^p spaces
Regularization and Approximation by Smooth Functions
Weak Derivatives
The Chain Rule
The W^(k,p) Spaces
Density Theorems
Imbedding Theorems
Potential Estimates and Imbedding Theorems
The Morrey and John-Nirenberg Estimes
Compactness Results
Difference Quotients
Extension and InterpolationNotesProblems
Generalized Solutions and Regularity
The Weak Maximum Principle
Solvability of the Dirichlet Problem
Diferentiability of Weak Solutions
Global Regularity
Global Boundedness of Weak Solutions
Local Properties of Weak Solutions
The Strong Maximum Principle
The Harnack Inequality
H+�lder Continuity
Local Estimates at the Boundary
H+�lder Estimates for the First Derivatives
The Eigenvalue ProblemNotesProblems
Strong Solutions
Maximum Princiles for Strong Solutions
L^p Estimates: Preliminary Analysis
The Marcinkiewicz Interpolation Theorem
The Calderon-Zygmund Inequality
L^p Estimates
The Dirichlet Problem
A Local Maximum Principle
H+�lder and Harnack Estimates
Local Estimates at the BoundaryNotesProblems
Quasilinear Equations
Maximum and Comparison Principles
The Comparison Principle
Maximum Principles
A Counterexample
Comparison Principles for Divergence Form Operators
Maximum Principles for Divergence Form Operators Notes Problems
Topological Fixed Point Theorems and Their Application
The Schauder Fixes Point Theorem
The Leray-Schauder Theorem: a Special Case
An Application
The Leray-Schauder Fixed Point Theorem
Variational ProblemsNotes
Equations in Two Variables
Quasiconformal Mappings
h+�lder Gradient Estimates for Linear Equations
The Dirichlet Problem for Uniformly Elliptic Equations
Non-Uniformly Elliptic EquationsNotesProblems
H+�lder Estimates for the Gradient
Equations of Divergence Form
Equations in Two Variables
Equations of General Form; the Interior Estimate
Equations of General Form; the Boundary Estimate
Application to the Dirichlet ProblemNotes
Boundary Gradient Estimates
General Domains
Convex Domains
Boundary Curvature Conditions
Non-Existence Results
Continuity Estimates
Appendix: Boundary Curvature and the Distance FunctionNotesProblems
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