Schauder Estimates for the Single Layer Potential in Hydrodynamics
Paul Deuring, Werner Varnhorn · Mathematische Nachrichten · 1992
Abstract Let Ω be an open set in ℝN(N ⩾ 3), with compact boundary ϑΩ of type C1,α(ϵ(0,1)). We show that the single layer potential Ef, related to the stationary Stokes system on Ω, belongs to C1,α(ϑΩ)N, provided the source density f belongs to Cα(ϑΩ)N. In addition, we prove a related estimate of the function E(f)ϑΩ and its tangential derivatives.