Schauder Estimates for the Single Layer Potential in Hydrodynamics

Let Ω be an open set in ?^N(N ? 3), with compact boundary ?Ω of type C^1,α(?(0,1)). We show that the single layer potential Ef, related to the stationary Stokes system on Ω, belongs to C^1,α(?Ω)^N, provided the source density f belongs to C^α(?Ω)^N. In addition, we prove a related estimate of the function E(f)_?Ω and its tangential derivatives.