The Dirichlet problem for Stokes equation in a domain exterior to an open surface

The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and C^α-smoothness (with α<1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.