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.