Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients

@article{Dong2019BoundaryLM,
  title={Boundary Lebesgue mixed-norm estimates for non-stationary Stokes systems with VMO coefficients},
  author={Hongjie Dong and Doyoon Kim and Tuoc Van Phan},
  journal={Communications in Partial Differential Equations},
  year={2019},
  volume={47},
  pages={1700 - 1731}
}
Abstract We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm -estimates hold for the spatial second-order derivatives of solutions, assuming the smallness of the mean oscillations of the coefficients with respect to the spatial variables in small cylinders. In the un-mixed norm case with the result is still new and provides local boundary Caccioppoli-type estimates… 

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