Gradient estimates for Stokes systems in domains

Jongkeun Choi; Hongjie Dong

Gradient estimates for Stokes systems in domains

Analysis of PDEs 2018-05-08 v1

Authors: Jongkeun Choi , Hongjie Dong

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 $(Du, p)$ .

Cite

@article{arxiv.1805.02506,
  title  = {Gradient estimates for Stokes systems in domains},
  author = {Jongkeun Choi and Hongjie Dong},
  journal= {arXiv preprint arXiv:1805.02506},
  year   = {2018}
}

Comments

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

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