On limit behavior of a solution to boundary value problem in a plane sector

Authors study a certain boundary value problem in Sobolev-Slobodetskii spaces with integral condition in a plane excluding a ray from origin. Using auxiliary problem in outside of a convex cone and the wave factorization concept, we construct a general solution and consider transfer to limit boundary value problem. It was shown that limit boundary value problem can be solvable only if the boundary function satisfies to a certain singular functional equatio

Distributions, non-smooth manifolds, transmutations and boundary value problems

One discusses the problem of constructing the theory of pseudo differential equations on manifoldswith a non-smooth boundary.Using special factorization principle and transmutation operators we consider some general boundary value problems for elliptic pseudo-differential equations in canonical non-smooth manifold

On the asymptotic expansion of certain plane singular integral operators

We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with border

On some discrete boundary value problems in canonical domains

We study some discrete boundary value problems for discrete elliptic pseudo-differential equations in a half-space. These statements are related with a special periodic factorization of an elliptic symbol and a number of boundary conditions depends on an index of periodic factorizatio