Nonlinear Neumann-Transmission Problems for Stokes and Brinkman Equations on Euclidean Lipschitz Domains

The purpose of this paper is to use a layer potential analysis and the Leray-Schauder degree theory to show an existence result for a nonlinear Neumann-transmission problem corresponding to the Stokes and Brinkman operators on Euclidean Lipschitz domains with boundary data in L-p spaces, Sobolev spaces, and also in Besov spaces.