Higher order elliptic operators of divergence form in C1 or Lipschitz domains

We consider a 2mth order elliptic operator of divergence form in a domain Ω of , whose leading coefficients are uniformly continuous. In the paper [Y. Miyazaki, The Lp theory of divergence form elliptic operators under the Dirichlet condition, J. Differential Equations 215 (2005) 320–356], we developed the Lp theory including the construction of Lp resolvents, assuming that the boundary of Ω is of class Cm+1. The purpose of this paper is to show that the Lp theory also holds when Ω is a C1 domain, applying the inequalities of Hardy type for the Sobolev spaces.