Shape optimization for the Stokes hemivariational inequality with slip boundary condition

The paper is devoted to the analysis of a hemivariational inequality problem for the stationary Stokes equations in a bounded planar domain with a nonmonotone and multivalued slip boundary condition. First, a result on the stability of solutions of the hemivariational inequality on variations of the domain is established. Then we provide the existence of a solution to optimal shape design problems of the stationary Stokes hemivariational inequality. We investigate the convergence of shape optimization problems for the penalized inequality when the penalty parameter tends to zero. Finally, we prove a convergence result for a finite element approximation of the shape optimization problem.