An explicit potential theory for the Stokes resolvent boundary value problems in three dimensions (Q810752)

The paper gives a representation of the solution of the resolvent problem for the Stokes-system \[ (\lambda I-\Delta)u+\nabla \pi =f,\quad div u=0,\quad u|_{\partial \Omega}=0 \] on bounded or exterior domains \(\Omega \subset {\mathbb{R}}^ 3\) by potential theoretic methods. This can be found also in \textit{P. Deuring} [Math. Methods Appl. Sci. 13, 323-333, and 335-349 (1990; Zbl 0726.35098 and Zbl 0726.35099)] together with explicit estimates in \(L_ p\)-spaces. The paper ends with boundary integral equations for the case \(f=0\) and Dirichlet- or Neumann type boundary conditions.