An algebra generated by general pseudodifferential boundary value problems in a cone

1993 ◽  
Vol 64 (6) ◽  
pp. 1313-1330 ◽  
Author(s):  
A. O. Derviz
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Pseudodifferential Boundary

COMPLETE SCALE OF ISOMORPHISMS FOR ELLIPTIC PSEUDODIFFERENTIAL BOUNDARY-VALUE PROBLEMS

2001 ◽  
Vol 64 (2) ◽  
pp. 409-422 ◽  
Author(s):  
A. KOZHEVNIKOV
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Pseudodifferential Boundary

The aim of the paper is to establish a complete scale of isomorphisms for elliptic pseudodifferential boundary value problems generated by the operators of the Boutet de Monvel algebra. The result is an extension of the corresponding known results on elliptic differential boundary value problems. Because for any elliptic pseudodifferential boundary value problem there exists a parametrix belonging to the Boutet de Monvel algebra, the proof presented is much shorter than the known proof for differential problems. Systems that are elliptic in the sense of Douglis and Nirenberg are also considered.

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