A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.