Electronic Journal of Differential Equations, Vol. 2006(2006), No. 83, pp. 1-19. Title: Singular perturbation problem for the incompressible Reynolds equation Authors: Ionel Ciuperca (Univ. Lyon1, France) Imad Hafidi (Insa de Lyon, France) Mohammed Jai (Insa de Lyon, France) Abstract: We study the asymptotic behavior of the solution of a Reynolds equation which describe the behavior of the fluid between two closes surfaces as the distance between the two surfaces locally tends to zero. Submitted January 5, 2006. Published July 21, 2006. Math Subject Classifications: 76D08, 35B25, 35B40. Key Words: Reynolds lubrication equation; weighted Sobolev Spaces; variational inequality; singular perturbation analysis; maximum principle.