$L^p$ solvability of the Stationary Stokes problem on domains with conical singularity in any dimension

Abstract

The Dirichlet boundary value problem for the Stokes operator with $L^p$ data in any dimension on domains with conical singularity (not necessary a Lipschitz graph) is considered. We establish the solvability of the problem for all $p\in (2-\epsilon ,\infty ]$ and also its solvability in $C(\overline{D})$ for the data in $C(\partial D)$