Karol’, A. I. Operator-valued pseudodifferential operators and the resolvent of a degenerate elliptic operator. (English. Russian original) Zbl 0553.35036 Math. USSR, Sb. 49, 553-567 (1984); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 562-575 (1983). Let Y be a smooth manifold with boundary X. Let A be an elliptic differential operator of order \(2\ell\) degenerated on X. The author constructs the parametrix for the Dirichlet problem using operator-valued pseudo-differential operators. Reviewer: Yu.V.Egorov Cited in 1 Review MSC: 35J70 Degenerate elliptic equations 35S05 Pseudodifferential operators as generalizations of partial differential operators 35A30 Geometric theory, characteristics, transformations in context of PDEs Keywords:parametrix; Dirichlet problem; operator-valued pseudo-differential operators PDFBibTeX XMLCite \textit{A. I. Karol'}, Math. USSR, Sb. 49, 553--567 (1984; Zbl 0553.35036); translation from Mat. Sb., Nov. Ser. 121(163), No. 4, 562--575 (1983) Full Text: DOI EuDML