The Lp boundary value problems on Lipschitz domains

Let Omega be a bounded Lipschitz domain in R-n. We develop a new approach to the invertibility on L-p (partial derivative Omega) of the layer potentials associated with elliptic equations and systems in Omega. As a consequence, for n >= 4 and 2(n - 1)/(n + 1) - epsilon < p < 2 where epsilon > 0 depends on Omega, we obtain the solvability of the L-p Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic equation are also established. (c) 2007 Elsevier Inc. All rights reserved.