Theory and Applications of Partial Differential Equations

  • Piero Bassanini
  • Alan R. Elcrat

Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 46)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Piero Bassanini, Alan R. Elcrat
    Pages 1-9
  3. Piero Bassanini, Alan R. Elcrat
    Pages 11-51
  4. Piero Bassanini, Alan R. Elcrat
    Pages 53-101
  5. Piero Bassanini, Alan R. Elcrat
    Pages 103-211
  6. Piero Bassanini, Alan R. Elcrat
    Pages 213-267
  7. Piero Bassanini, Alan R. Elcrat
    Pages 269-289
  8. Piero Bassanini, Alan R. Elcrat
    Pages 291-394
  9. Piero Bassanini, Alan R. Elcrat
    Pages 395-435
  10. Back Matter
    Pages 437-444

About this book


This book is a product of the experience of the authors in teaching partial differential equations to students of mathematics, physics, and engineering over a period of 20 years. Our goal in writing it has been to introduce the subject with precise and rigorous analysis on the one hand, and interesting and significant applications on the other. The starting level of the book is at the first-year graduate level in a U.S. university. Previous experience with partial differential equations is not required, but the use of classical analysis to find solutions of specific problems is not emphasized. From that perspective our treatment is decidedly theoretical. We have avoided abstraction and full generality in many situations, however. Our plan has been to introduce fundamental ideas in relatively simple situations and to show their impact on relevant applications. The student is then, we feel, well prepared to fight through more specialized treatises. There are parts of the exposition that require Lebesgue integration, distributions and Fourier transforms, and Sobolev spaces. We have included a long appendix, Chapter 8, giving precise statements of all results used. This may be thought of as an introduction to these topics. The reader who is not familiar with these subjects may refer to parts of Chapter 8 as needed or become somewhat familiar with them as prerequisite and treat Chapter 8 as Chapter O.


Sobolev space differential equation mathematical physics partial differential equation

Authors and affiliations

  • Piero Bassanini
    • 1
  • Alan R. Elcrat
    • 2
  1. 1.University of Rome “La Sapienza”RomeItaly
  2. 2.Wichita State UniversityWichitaUSA

Bibliographic information