Influence of Nonisolated Singularities in a Lower-Order Coefficient of the Bitsadze Equation on the Statement of Boundary Value Problems

Abstract

We study the influence of nonisolated singularities (i.e., singularities along closed lines lying inside the domain) in the lower-order coefficients of the Bitsadze equation on the statement of boundary value problems. We discover that the conditions on the boundary of the domain in the Riemann–Hilbert problem are not sufficient for the solution; therefore, we consider a problem that combines elements of the Riemann–Hilbert problem on the boundary of the domain and the linear conjugation problem on the circles that support the singularities of the coefficients lying inside the domain. Using an appropriate refinement of Kellogg’s theorem on the conformal mapping of this domain onto a disk, we study the solvability of the problem