Partial Differential Operators of Elliptic Type

This book, which originally appeared in Japanese, was written for use in an undergraduate course of 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 ellipticity for higher order operators. Shimakura discusses the laplacian in Euclidean spaces, elementary solutions, smoothness of solutions, Vishik-Sobolev problems, the Scauder theory, and degenerate elliptic operators. The appendix covers such preliminaries as ordinary differential equations, Sobolev spaces, and maximum priniciples. 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.Shimakura, N. is the author of 'Partial Differential Operators of Elliptic Type' with ISBN 9780821845561 and ISBN 082184556X.