On the Solvability of Schwarz Problems for the Inhomogeneous Cauchy–Riemann and Polyanalytic Equations

In this work, we study the boundary behavior of the Schwarz-type and T-type operators in a partial eclipse domain. Particular emphasis is placed on the existence and regularity of boundary values at corner points of the domain, where classical smoothness assumptions may fail. We establish the continuity of the associated integral operators up to the boundary and prove the existence of non-tangential limits at these singular points. Furthermore, we study a Schwarz-type boundary problem associated with an inhomogeneous polyanalytic equation posed in a partial-eclipse-shaped domain and derive an explicit formula for all its solutions.