This paper considers to the equation [\int_{S} \frac{U(Q)}{|P-Q|^{N-1}} dS(Q)
= F(P), P \in S,] where the surface S is the graph of a Lipschitz function \phi
on R^N, which has a small Lipschitz constant. The integral in the left-hand
side is the single layer potential corresponding to the Laplacian in R^{N+1}.
Let \Lambda(r) be a Lipschitz constant of \phi on the ball centered at the
origin with radius 2r. Our analysis is carried out in local L^p-spaces and
local Sobolev spaces, where 1 < p < \infty, and results are presented in terms
of \Lambda(r). Estimates of solutions to the equation are provided, which can
be used to obtain knowledge about the behaviour of the solutions near a point
on the surface. The estimates are given in terms of seminorms. Solutions are
also shown to be unique if they are subject to certain growth conditions. Local
estimates are provided and some applications are supplied.