Solvability of a boundary value problem for steady Stokes equations in a sectorial domain

We investigate a boundary value problem for steady Stokes equations in a sectorial domain. The problem appears in the analysis of a free boundary problem for Navier–Stokes equations that describe the non-steady motion of an incompressible viscous capillary fluid with moving contact points. We prove the existence of a unique solution in weighted Sobolev spaces and derive estimates in the norms of these spaces.