A Mixed Problem for a Plane with Rectilinear Cuts

We solve a mixed problem for a plane $u^{+}(t)=f^{+}(t)$, $v^{-}(t)=g^{-}(t)$, $t\in L$, where $L$ is the union of a finite or denumerable set of segments (including those arranged periodically) with an accumulation point at infinity. For a denumerable set of segments, the problem is solved by the reduction to the corresponding Riemann problem in the case of a denumerable set of circuits, including those arranged periodically.