**Translations of Mathematical Monographs**

1992;
288 pp;
Hardcover

MSC: Primary 35;
**Print ISBN: 978-0-8218-4556-1
Product Code: MMONO/99**

List Price: $120.00

Individual Member Price: $96.00

# Partial Differential Operators of Elliptic Type

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*Norio Shimakura*

This book, which originally appeared in Japanese, was written for use in an undergraduate course or first year graduate course in partial differential equations and is likely to be of interest to researchers as well. This book presents a comprehensive study of the theory of elliptic partial differential operators. Beginning with the definitions of ellipticity for higher order operators, Shimakura discusses the Laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Schauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum principles. Because elliptic operators arise in many areas, readers will appreciate this book for the way it brings together a variety of techniques that have arisen in different branches of mathematics.

#### Readership

First year graduate students specializing in partial differential equations, researchers in other fields of mathematics.

#### Reviews & Endorsements

The book was designed for seniors or first-year graduate students in Sendai specializing in elliptic partial differential equations, and will fill the same role admirably today in America or anywhere.

-- Mathematical Reviews

Clear, well written, interesting; although it is addressed to (undergraduate or graduate) students, it is certainly useful for partial differential equations researchers as well.

-- Zentralblatt MATH