Book Volume 214 2013

Partial Differential Equations


ISBN: 978-1-4614-4808-2 (Print) 978-1-4614-4809-9 (Online)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiii

  2. Chapter

    Pages 1-7

    Introduction: What Are Partial Differential Equations?

  3. Chapter

    Pages 9-35

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

  4. Chapter

    Pages 37-57

    The Maximum Principle

  5. Chapter

    Pages 59-83

    Existence Techniques I: Methods Based on the Maximum Principle

  6. Chapter

    Pages 85-126

    Existence Techniques II: Parabolic Methods. The Heat Equation

  7. Chapter

    Pages 127-148

    Reaction–Diffusion Equations and Systems

  8. Chapter

    Pages 149-172

    Hyperbolic Equations

  9. Chapter

    Pages 173-206

    The Heat Equation, Semigroups, and Brownian Motion

  10. Chapter

    Pages 207-213

    Relationships Between Different Partial Differential Equations

  11. Chapter

    Pages 215-253

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

  12. Chapter

    Pages 255-309

    Sobolev Spaces and L 2 Regularity Theory

  13. Chapter

    Pages 311-328

    Strong Solutions

  14. Chapter

    Pages 329-351

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

  15. Chapter

    Pages 353-392

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

  16. Back Matter

    Pages 393-410