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Lectures on Elliptic and Parabolic Equations in Hölder Spaces
N. V. Krylov, University of Minnesota, Minneapolis, MN

Graduate Studies in Mathematics
1996; 164 pp; hardcover
Volume: 12
Reprint/Revision History:
reprinted with corrections 1997
ISBN-10: 0-8218-0569-X
ISBN-13: 978-0-8218-0569-5
List Price: US$36
Member Price: US$28.80
Order Code: GSM/12
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These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in Hölder spaces. Krylov shows that this theory--including some issues of the theory of nonlinear equations--is based on some general and extremely powerful ideas and some simple computations.

The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed.

This book, with nearly 200 exercises, will provide a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.


Graduate students and researchers in mathematics, physics, and engineering interested in the theory of partial differential equations.


"Short but not condensed, well organized and gives a stimulating presentation of basic aspects of the theory of elliptic and parabolic equations in Hölder spaces ... an interesting addition for students and instructors."

-- Zentralblatt MATH

"The author has fully achieved his goal ... and has written an impressive book that presents nice material in an interesting way ... this book can be recommended as a thorough, modern and sufficiently broad introduction to partial differential equations of elliptic and parabolic types for graduate students and instructors (and also for individual study) in mathematics, physics, and (possibly) engineering."

-- Mathematical Reviews

Table of Contents

  • Lectures on elliptic and parabolic equations in Hölder spaces
  • Elliptic equations with constant coefficients in \(\mathbb{R}^d\) (Chapter 1)
  • Laplace's equation (Chapter 2)
  • Solvability of elliptic eqauations with constant coefficients in the Hölder spaces (Chapter 3)
  • Elliptic equations with variable coefficients in \(\mathbb{R}^d\) (Chapter 4)
  • Second-order elliptic equations in half spaces (Chapter 5)
  • Second-order elliptic equations in smooth domains (Chapter 6)
  • Elliptic equations in non-smooth domains (Chapter 7)
  • Parabolic equations in the whole space (Chapter 8)
  • Boundary-value problems for parabolic equations in half spaces (Chapter 9)
  • Parabolic equations in domains (Chapter 10)
  • Bibliography
  • Index
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