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arXiv · 1303.1854

Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains

William M. Feldman
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Abstract

We prove the homogenization of the Dirichlet problem for fully nonlinear elliptic operators with periodic oscillation in the operator and of the boundary condition for a general class of smooth bounded domains. This extends the previous results of Barles and Mironescu in half spaces. We show that homogenization holds despite a possible lack of continuity in the homogenized boundary data. The proof is based on a comparison principle with partial Dirichlet boundary data which is of independent interest.

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William M. Feldman. 2013-03-07. Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains. https://arxiv.org/abs/1303.1854

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