The Lp Dirichlet problem for elliptic systems on Lipschitz domains

Abstract

We develop a new approach to the Lp Dirichlet problem via L 2 estimates and reverse Holder inequalities. We apply this approach to second order elliptic systems and the polyharmonic equation on a bounded Lipschitz domain Ω in ℝn. For n > 4 and 2 - ε < p < 2(n-1)/n-3 + ε, we establish the solvability of the Dirichlet problem with boundary data in Lp(∂Ω). In the case of the polyharmonic equation Δlu = 0 with l ≥ 2, the range of p is sharp if 4 ≤ n < 2l + 1. © International Press 2006.