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

We 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.

Automated summary

The study focuses on a boundary value problem in Sobolev-Slobodetskii spaces with an integral condition, excluding a ray from the origin on a plane. By utilizing an auxiliary problem outside a convex cone and the concept of wave factorization, a general solution is constructed and the transition to the limit boundary value problem is considered. It is demonstrated that the limit boundary value problem can only be solvable if the boundary function satisfies a specific singular functional equation.