A free-boundary problem in theory of lubrication

Abstract

We study a problem related to the lubrication with cavitation arising in bearings. This problem was previously studied by {\it G. Bayada} and {\it M. Chambat} [Boll. Unione Mat. Ital., IV. Ser., B 3, 543-557 (1984)]. They stated the problem and proved the existence of solutions; they proved uniqueness of solutions, under regularity assumptions on the free boundary.\par The goal of this paper is to prove comparison and uniqueness of solutions without assuming condition related to the free boundary.