The Lp Dirichlet problem for elliptic systems on Lipschitz domains

We develop a new approach to the LP Dirichlet problem via L-2 es timates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain Omega in R-n. For n >= 4 and 2 - epsilon < p < 2(n-1)/n-3 + epsilon, we establish the solvability of the Dirichlet problem with boundary data in L-p (partial derivative Omega). In the case of the polyharmonic equation Delta(l)u = 0 with l >= 2, the range of p is sharp if 4 <= n <= 2l + 1.