We consider a nonlinear Neumann problem, with periodic oscillation in the elliptic operator and on the boundary condition. Our focus is on problems posed in half-spaces, but with general normal directions that may not be parallel to the directions of periodicity. As the frequency of the oscillation grows, quantitative homogenization results are derived. When the homogenized operator is rotation-invariant, we prove the Hölder continuity of the homogenized boundary data. While we follow the outline of , new challenges arise due to the presence of tangential derivatives on the boundary condition in our problem. In addition we improve and optimize the rate of convergence within our approach. Our result appear to be new even for the linear oblique problem.
MSC Codes 35J60
|Original language||English (US)|
|State||Published - Nov 15 2019|
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