Solutions to the Poisson equation in L_p weighted spaces for p \geq 2

We examine the Poisson equation with boundary condition on cylinder in R3 in weighted spaces of L_p type, with p\geq 2. The weight is given as a distance from a distinguished plane in some positive power. We treat in different way p=2 and p\geq 3 cases. The motivation of the problem is the analysis of the inflow-outflow motion described with Navier-Stokes equations.