Partial Differential Equations

Chapter 1 Introduction: What Are Partial Differential Equations?

Chapter 2 The Laplace Equation as the Prototype of an Elliptic Partial Differential Equation of Second Order

Chapter 3 The Maximum Principle

Chapter 4 Existence Techniques I: Methods Based on the Maximum Principle

Chapter 5 Existence Techniques II: Parabolic Methods. The Heat Equation

Chapter 6 The Wave Equation and Its Connections with the Laplace and Heat Equations

Chapter 7 The Heat Equation, Semigroups, and Brownian Motion

Chapter 8 The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)

Chapter 9 Sobolev Spaces and L 2 Regularity Theory

Chapter 10 Strong Solutions

Chapter 11 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)