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

Abstract

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 equation