A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in R3. Issue 9 (13th June 2019)

• Record Type: Journal Article
• Authors: Albişoru, Andrei‐Florin
• Is Part Of: Mathematische Nachrichten. Volume 292:Issue 9(2019)
• Page Start: 1876
• Page End: 1896
• Publication Date: 2019-06-13
• Subjects: Brinkman system -- Fredholm operator -- layer potentials -- Lipschitz domains in R3 -- Sobolev spaces -- transmission problems -- 35J25 -- 35Q35 -- 46E35; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201800139
• Languages: English
• ISSNs: 0025-584X

Abstract

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.