Geodesic
The Inhomogeneous Dirichlet Problem for the Stokes System in Lipschitz Domains with Unit Normal Close to~VMO
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 65-88

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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.
Keywords: Stokes system, Lipschitz domain, boundary value problem, Besov–Triebel–Lizorkin spaces. 
@article{FAA_2009_43_3_a5,
     author = {V. G. Maz'ya and M. Mitrea and T. O. Shaposhnikova},
     title = {The {Inhomogeneous} {Dirichlet} {Problem} for the {Stokes} {System} in {Lipschitz} {Domains} with {Unit} {Normal} {Close} {to~VMO}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {65--88},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_3_a5/}
}
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V. G. Maz'ya; M. Mitrea; T. O. Shaposhnikova. The Inhomogeneous Dirichlet Problem for the Stokes System in Lipschitz Domains with Unit Normal Close to~VMO. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 3, pp. 65-88. http://geodesic.mathdoc.fr/item/FAA_2009_43_3_a5/