The Lp boundary value problems on Lipschitz domains

Let Ω be a bounded Lipschitz domain in Rn. We develop a new approach to the invertibility on Lp(∂Ω) of the layer potentials associated with elliptic equations and systems in Ω. As a consequence, for n⩾4 and where ε>0 depends on Ω, we obtain the solvability of the Lp Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic equation are also established.