Conormal derivative problems for stationary Stokes system in Sobolev spaces
Jongkeun Choi, Hongjie Dong, Doyoon Kim · Discrete and Continuous Dynamical Systems · 2018
We prove the solvability in Sobolev spaces of the conormal derivative problem for the stationary Stokes system with irregular coefficients on bounded Reifenberg flat domains. The coefficients are assumed to be merely measurable in one direction, which may differ depending on the local coordinate systems, and have small mean oscillations in the other directions. In the course of the proof, we use a local version of the Poincaré inequality on Reifenberg flat domains, the proof of which is of independent interest.