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In this article we investigate averaging properties of fully nonlinear PDEsin bounded domains with oscillatory Neumann boundary data. The oscillation isperiodic and is present both in the operator and in the Neumann data. Our mainresult states that, when the domain does not have flat boundary parts and whenthe homogenized operator is rotation invariant, the solutions uniformlyconverge to the homogenized solution solving a Neumann boundary problem.Furthermore we show that the homogenized Neumann data is continuous withrespect to the normal direction of the boundary.

Homogenization for nonlinear PDEs in general domains with oscillatory Neumann boundary data