Regularity of solutions to a lubrication problem with discountinuous separation data

Abstract

We study the regularity of the solution to the Reynolds equation for incompressible and compressible fluids when the gap between the lubricated surfaces, “h(x,y)”, presents a discontinuity in a two-dimensional bounded domain. As in the one-dimensional problem studied by Rayleigh, the solution P does not belong to C1(Ω) but we obtain that | P| is bounded, i.e. P W1,∞(Ω).