Partial Differential Equations

Second Edition

  • Emmanuele DiBenedetto

Part of the Cornerstones book series (COR)

Table of contents

  1. Front Matter
    Pages 1-20
  2. Emmanuele DiBenedetto
    Pages 1-16
  3. Emmanuele DiBenedetto
    Pages 37-86
  4. Emmanuele DiBenedetto
    Pages 87-107
  5. Emmanuele DiBenedetto
    Pages 109-134
  6. Emmanuele DiBenedetto
    Pages 135-181
  7. Emmanuele DiBenedetto
    Pages 183-224
  8. Emmanuele DiBenedetto
    Pages 225-263
  9. Emmanuele DiBenedetto
    Pages 265-295
  10. Emmanuele DiBenedetto
    Pages 297-345
  11. Emmanuele DiBenedetto
    Pages 347-371
  12. Back Matter
    Pages 1-17

About this book


This self-contained textbook offers an elementary introduction to partial differential equations (PDEs), primarily focusing on linear equations, but also providing a perspective on nonlinear equations, through Hamilton--Jacobi equations, elliptic equations with measurable coefficients and DeGiorgi classes. The exposition is complemented by examples, problems, and solutions that enhance understanding and explore related directions.

Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct misprints, and improve clarity. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists.

The newly added three last chapters, on first order non-linear PDEs (Chapter 8), quasilinear elliptic equations with measurable coefficients (Chapter 9) and DeGiorgi classes (Chapter 10), point to issues and directions at the forefront of current investigations.

Reviews of the first edition:

The author's intent is to present an elementary introduction to PDEs... In contrast to other elementary textbooks on PDEs . . . much more material is presented on the three basic equations: Laplace's equation, the heat and wave equations. . . . The presentation is clear and well organized. . . . The text is complemented by numerous exercises and hints to proofs.

---Mathematical Reviews

This is a well-written, self-contained, elementary introduction to linear, partial differential equations.

---Zentralblatt MATH


Boundary value problem Cauchy--Kowalewski Theorem Conservation Laws Degiorgi Classes Elliptic Theory Green's Theorem Linear Elliptic Equations Partial Differential Equations Potential Viscosity Solutions partial differential equation wave equation

Authors and affiliations

  • Emmanuele DiBenedetto
    • 1
  1. 1.Dept. MathematicsVanderbilt UniversityNashvilleU.S.A.

Bibliographic information

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