$L_p$ regularity theorem for elliptic equations in less smooth domains
$L_p$ regularity theorem for elliptic equations in less smooth domains
We consider a $2m$th-order strongly elliptic operator $A$ subject to Dirichlet boundary conditions in a domain $\Omega$ of $\mathbb{R}^{n}$, and show the $L_{p}$ 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 …