Recent Developments on Pseudo-Differential Operators (I)

10.5556/j.tkjm.46.2015.1707

D. C. Chang；W. Rungrottheera；B. W. Schulze

Tamkang Journal of Mathematics

46卷1期（2015 / 03 / 01）

1 - 30

英文

In recent years the analysis of (pseudo-)differential operators on manifolds with second and higher order corners made considerable progress, and essential new structures have been developed. The main objective of this series of paper is to give a survey on the development of this theory in the past twenty years. We start with a brief background of the theory of pseudo-differential operatorswhich including its symbolic calculus on Rn. Next we introduce pseudo-differential calculus with operator-valued symbols. This allows us to discuss elliptic boundary value problems on smooth domains in Rn and elliptic problems on manifolds. This paper is based on the first part of lectures given by the authors while they visited the National Center for Theoretical Sciences in Hsinchu, Taiwan duringMay-July of 2014.