Mixed boundary value problems for the stokes system

We prove the well-posedness of the mixed problem for the Stokes system in a class of Lipschitz domains in ℝⁿ, n ≥ 3. The strategy is to reduce the original problem to a boundary integral equation, and we establish certain new Rellich-type estimates which imply that the intervening boundary integral operator is semi-Fredholm. We then prove that its index is zero by performing a homotopic deformation of it onto an operator related to the Lamesystem, which has recently been shown to be invertible.