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Elliptic Partial Differential Equations of Second Order

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Cover of 'Elliptic Partial Differential Equations of Second Order'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Laplace’s Equation
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    Chapter 3 The Classical Maximum Principle
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    Chapter 4 Poisson’s Equation and the Newtonian Potential
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    Chapter 5 Banach and Hilbert Spaces
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    Chapter 6 Classical Solutions; the Schauder Approach
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    Chapter 7 Sobolev Spaces
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    Chapter 8 Generalized Solutions and Regularity
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    Chapter 9 Strong Solutions
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    Chapter 10 Maximum and Comparison Principles
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    Chapter 11 Topological Fixed Point Theorems and Their Application
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    Chapter 12 Equations in Two Variables
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    Chapter 13 Hölder Estimates for the Gradient
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    Chapter 14 Boundary Gradient Estimates
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    Chapter 15 Global and Interior Gradient Bounds
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    Chapter 16 Equations of Mean Curvature Type
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    Chapter 17 Fully Nonlinear Equations
Attention for Chapter 9: Strong Solutions
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