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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 Reaction–Diffusion Equations and Systems
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    Chapter 7 Hyperbolic Equations
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    Chapter 8 The Heat Equation, Semigroups, and Brownian Motion
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    Chapter 9 Relationships Between Different Partial Differential Equations
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    Chapter 10 The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)
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    Chapter 11 Sobolev Spaces and L 2 Regularity Theory
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    Chapter 12 Strong Solutions
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    Chapter 13 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)
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    Chapter 14 The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash
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