Open AccessRecent developments on Pseudo-Differential Operators (I)
Author(s) -
Der–Chen Chang,
W. Rungrottheera,
Bert-Wolfgang Schulze
Publication year - 2015
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.46.2015.1707
Subject(s) - mathematics , differential operator , differential (mechanical device) , elliptic operator , calculus (dental) , operator (biology) , algebra over a field , order (exchange) , center (category theory) , differential calculus , pure mathematics , medicine , biochemistry , chemistry , dentistry , finance , repressor , transcription factor , engineering , economics , gene , crystallography , aerospace engineering
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 operators which including its symbolic calculus on $\R^n$. Next we introduce pseudo-differential calculus with operator-valued symbols. This allows us to discuss elliptic boundary value problems on smooth domains in $\R^n$ 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 during May-July of 2014.