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Elliptic operators on the manifolds with edge singularities. (English. Russian original) Zbl 0959.58037
Dokl. Math. 58, No. 3, 363-366 (1998); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 363, No. 1, 30-33 (1998).
From the paper: This communication is a continuation of the paper [B. Yu. Sternin, V. E. Shatalov and B.-W. Schulze, Dokl. Akad. Nauk 362, No. 4, 453-455 (1998)], in which elliptic equations defined on the manifolds with point singularities of the cusp type were studied and, in particular, the operator algebra corresponding to such singularities was constructed. Here, we perform similar constructions for the case when the manifold under consideration contains edges consisting of the points of the aforementioned type. As a means for constructing the operator algebra, we again use the Maslov operator calculus.
MSC:
58J32 Boundary value problems on manifolds
58J05 Elliptic equations on manifolds, general theory
35J40 Boundary value problems for higher-order elliptic equations
58J42 Noncommutative global analysis, noncommutative residues
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