A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in R3. Issue 9 (13th June 2019) - Albişoru, Andrei‐Florin
Abstract: 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 R 3, the former being bounded, and the latter, its complement in R 3 . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in R 3 by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L 2 ‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.