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 $(Du,p)$.

arXiv comment23 pages. arXiv admin note: text overlap with arXiv:1803.05560

References in corpus (3)

• Gradient estimates for parabolic and elliptic systems from linear laminates
• On $C^1$, $C^2$, and weak type-$(1,1)$ estimates for linear elliptic operators
• Gradient estimates for Stokes systems with Dini mean oscillation coefficients