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This article is cited in 5 scientific papers (total 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.
Received: 10.07.1982
Citation:
A. I. Karol', “Operator-valued pseudodifferential operators and the resolvent of a degenerate elliptic operator”, Mat. Sb. (N.S.), 121(163):4(8) (1983), 562–575; Math. USSR-Sb., 49:2 (1984), 553–567
Linking options:
https://www.mathnet.ru/eng/sm2225https://doi.org/10.1070/SM1984v049n02ABEH002727 https://www.mathnet.ru/eng/sm/v163/i4/p562
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Abstract page: | 362 | Russian version PDF: | 199 | English version PDF: | 6 | References: | 53 |
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