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Partial Differential Equations

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Cover of 'Partial Differential Equations'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction: What Are Partial Differential Equations?
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    Chapter 2 The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order
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    Chapter 3 The Maximum Principle
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    Chapter 4 Existence Techniques I: Methods Based on the Maximum Principle
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    Chapter 5 Existence Techniques II: Parabolic Methods. The Heat Equation
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    Chapter 6 The Wave Equation and Its Connections with the Laplace and Heat Equations
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    Chapter 7 The Heat Equation, Semigroups, and Brownian Motion
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    Chapter 8 The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)
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    Chapter 9 Sobolev Spaces and L 2 Regularity Theory
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    Chapter 10 Strong Solutions
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    Chapter 11 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)
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    Chapter 12 The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash
Attention for Chapter 1: Introduction: What Are Partial Differential Equations?
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