arXiv:1805.02506 Abstract | arXiv Analytics

arXiv:1805.02506 [math.AP]Abstract References Reviews Resources

Gradient estimates for Stokes systems in domains

Published 2018-05-04Version 1

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 $(Du, p)$.

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

Categories: math.AP

Subjects: 76D07, 35B65, 35J57

Keywords: gradient estimates, dini mean oscillation coefficients, zero dirichlet boundary condition, stationary stokes system, weak solution

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