On the Stokes system and on the biharmonic equation in the half‐space: an approach via weighted Sobolev spaces
Tahar Zamène Boulmezaoud · Mathematical Methods in the Applied Sciences · 2002
Abstract In this paper, we investigate the Stokes system and the biharmonic equation in a half‐space of ℝn. Our approach rests on the use of a family of weighted Sobolev spaces as a framework for describing the behaviour at infinity. A complete class of existence, uniqueness and regularity results for both the problems is proved. The proofs are mainly based on the principle of reflection. Copyright © 2002 John Wiley & Sons, Ltd.