Elliptic boundary value problems on manifolds with a piecewise smooth boundary

In this paper general boundary value problems for second-order elliptic differential equations are considered on manifolds with edges. It is assumed that in the neighborhood of an edge point the manifold is diffeomorphic to the interior of a convex dihedral angle. Effective conditions for normal solvability of these boundary value problems are obtained and the parametrix is constructed. The methods make use of the theory of analytic functions of several variables and automorphic functions.
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