Potential techniques for boundary value problems on C1-domains

In troduct ion In this work we consider the Dirichlet and Neumann problems for Laplace's equation in a bounded domain, D, of R ' , n >~ 3. Assuming the boundary, ~D, to be of class C 1 and the boundary data in/2 '(~D), 1 < p < 0% we resolve the above problems in the form of classical double and single layer potentials respectively. More precisely, given g ELr(8D) we find a solution to the I)irichlet problem,