Gradient estimates for Stokes systems in domains

Abstract

We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having $C^{1,\mathrm{Dini}}$ boundary. We prove that if $(u,p)$ is a weak solution of the system with zero Dirichlet boundary condition, then $(Du,p)$ is continuous up to the boundary. We also prove a weak type-$(1,1)$ estimate for $(Du,p)$.

23 pages. arXiv admin note: text overlap with arXiv:1803.05560