Gradient estimates for Stokes systems in domains

Published 4 May 2018 in math.AP | (1805.02506v1)

Abstract: We study the stationary Stokes system with Dini mean oscillation coefficients in a domain having $C^{{1,\rm{Dini}}$} 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 $(Du, p)$.

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