Regularity of Solutions to the Stokes Equations under a Certain Nonlinear Boundary Condition

The regularity of a solution to the variational inequality for the Stokes equation is considered. The inequality describes the steady motion of the viscous incompressible uid under a certain unilateral constrain of friction type. Firstly the solution is approximated by solutions to a regularized problem which is introduced by Yosida's regularization for a multi-valued opearator. Then we establish a regularity result to the regularized problem. The regularity of the solution to the original inequality follows by the limiting argument.