Single layer potentials on surfaces with small Lipschitz constants

This paper considers to the equation∫SU(Q)|P−Q|N−1dS(Q)=F(P),P∈S, where the surface S is the graph of a Lipschitz function φ on RN, which has a small Lipschitz constant. The integral on the left-hand side is the single layer potential corresponding to the Laplacian in RN+1. Let Λ(r) be the Lipschitz constant of φ on the ball centered at the origin with radius 2r. Our analysis is carried out in local Lp-spaces and local Sobolev spaces, where 1