# Boundary Value Problems for the Stokes System in Arbitrary Lipschitz Domains

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*Marius Mitrea; Matthew Wright*

A publication of the Société Mathématique de France

The goal of this work is to treat the following main boundary value
problems for the Stokes system: (1) the Dirichlet problem with
\(L^p\)-data and nontangential maximal function estimates, (2) the
Neumann problem with \(L^p\)-data and nontangential maximal
function estimates, (3) the Regularity problem with \(L^p_1\)-data
and nontangential maximal function estimates, (4) the transmission problem
with \(L^p\)-data and nontangential maximal function estimates,
(5) the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin
spaces, and (6) the Poisson problem with Neumann condition in
Besov-Triebel-Lizorkin spaces, in Lipschitz domains of arbitrary
topology in \({\mathbb{R}}^n\), for each \(n\geq2\).

The authors' approach relies on boundary integral methods and yields
constructive solutions to the aforementioned problems.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

#### Readership

Graduate students and research mathematicians interested in the Stokes system, Lipschitz domains, boundary problems, layer potentials, and Besov-Triebel-Lizorkin spaces.