This article is cited in 5 papers

Operator-valued pseudodifferential operators and the resolvent of a degenerate elliptic operator

A. I. Karol'


Abstract: In this paper the author constructs an asymptotic expansion of the resolvent of the operator of the Dirichlet problem for an elliptic equation of divergence form with a power degeneracy on the boundary. To construct the expansion a variant of the technique of pseudodifferential operators ($\Psi$DO's) with operator-valued symbols is used, in combination with the technique of “ordinary” scalar $\Psi$DO's. The difference between the resolvent and the approximation thus obtained is an integral operator whose kernel decreases at infinity faster than any power of the spectral parameter. In a neighborhood of the boundary this operator smooths only in directions tangent to the boundary.
Bibliography: 16 titles.

UDC: 517.9

MSC: Primary 35J70; Secondary 35P20

Received: 10.07.1982

 English version: Mathematics of the USSR-Sbornik, 1984, 49:2, 553–567

Bibliographic databases:

• 
•