The Inhomogeneous Dirichlet Problem for the Stokes System in Lipschitz Domains with Unit Normal Close to~VMO

V. G. Maz'ya ; M. Mitrea ; T. O. Shaposhnikova

Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 65-88.

Résumé

The goal of this work is to study the inhomogeneous Dirichlet problem for the Stokes system in a Lipschitz domain $\Omega\subseteq\mathbb{R}^n$, $n\ge 2$. Our main result is that this problem is well posed in Besov–Triebel–Lizorkin spaces, provided that the unit normal $\nu$ to $\Omega$ has small mean oscillation.

Détail

Keywords: Stokes system, Lipschitz domain, boundary value problem, Besov–Triebel–Lizorkin spaces.

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