LAUSR

We consider a 2mth-order strongly elliptic operator A subject to Dirichlet boundary conditions in a domain Ω of Rn, and show the Lp regularity theorem, assuming that the domain has less smooth boundary. We derive the regularity theorem from the following isomorphism theorems in Sobolev spaces. Let k be a nonnegative integer. When A is a divergence form elliptic operator, A − λ has a bounded inverse from the Sobolev space Wk−m p (Ω) into W k+m p (Ω) for λ belonging to a suitable sectorial region of the complex plane, if Ω is a uniformly Ck,1 domain. When A is a nondivergence form elliptic operator, A − λ has a bounded inverse from Wk p (Ω) into W p (Ω), if Ω is a uniformly C k+m,1 domain. Compared with the known results, we weaken the smoothness assumption on the boundary of Ω by m− 1.