Higher order elliptic operators of divergence form in [formula omitted] or Lipschitz domains

Abstract

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