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 Reaction–Diffusion Equations and Systems

Chapter 7 Hyperbolic Equations

Chapter 8 The Heat Equation, Semigroups, and Brownian Motion

Chapter 9 Relationships Between Different Partial Differential Equations

Chapter 10 The Dirichlet Principle. Variational Methods for the Solution of PDEs (Existence Techniques III)

Chapter 11 Sobolev Spaces and L 2 Regularity Theory

Chapter 13 The Regularity Theory of Schauder and the Continuity Method (Existence Techniques IV)

Chapter 14 The Moser Iteration Method and the Regularity Theorem of de Giorgi and Nash