On some estimates of the pressure for the Stokes equations in an infinite sector

Abstract

Some \textit{a priori} estimates of the pressure for the Stokes equations in an infinite sector with the slip and the stress conditions on the boundary are established in weighted Sobolev spaces. The estimates for its higher order derivatives are obtained by the general scheme of Kondrat’ev. Instead the estimates for the lower order ones are derived by making use of the Mellin transformation and the explicit representation formula of the pressure.