Mixed boundary value problems for the Navier-Stokes system in polyhedral   domains
  Mixed boundary value problems for the Navier-Stokes system in a polyhedral domain are considered. Different boundary conditions (in particular, Dirichlet, Neumann, slip conditions) are prescribed on the faces of a polyhedron. The authors obtain regularity results for weak solutions in weighted (and non-weighted) L_p Sobolev and H\"older spaces. 
V. G. Maz'ya, J. Rossmann