Jongkeun Choi, Hongjie Dong, Doyoon Kim
Published 2018-04-27Version 1
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the Stokes system are continuous in the interior of the domain. Also, we establish the global pointwise bound for the Green function under the additional assumption that weak solutions of the conormal derivative problem for the Stokes system are locally bounded up to the boundary. We provide some examples satisfying such continuity and boundedness properties.
Conormal derivative problems for stationary Stokes system in Sobolev spaces
Weighted $L_q$-estimates for stationary Stokes system with partially BMO coefficients
$L_q$-estimates for stationary Stokes system with coefficients measurable in one direction
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