Newtonian and single layer potentials for the Stokes system with $L^{\infty }$ coefficients and the exterior Dirichlet problem

Abstract

A mixed variational formulation of some problems in $L^2$-based Sobolev spaces is used to define the Newtonian and layer potentials for the Stokes system with $L^{\infty }$ coefficients on Lipschitz domains in ${\mathbb{R}}^3$. Then the solution of the exterior Dirichlet problem for the Stokes system with $L^{\infty }$ coefficients is presented in terms of these potentials and the inverse of the corresponding single layer operator.

20 pages