Homogenization of the oscillating Dirichlet boundary condition in general domains

作者：Feldman William M^*

来源：Journal de Mathematiques Pures et Appliquees, 2014, 101(5): 599-622.

DOI：10.1016/j.matpur.2013.07.003

• Homogenization
• Discontinuous boundary data
• Fully nonlinear elliptic equations
• Boundary layers

We prove the homogenization of the Dirichlet problem for fully nonlinear uniformly elliptic operators with periodic oscillation in the operator and in the boundary condition for a general class of smooth bounded domains. This extends the previous results of Barles and Mironescu (2012) [4] 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.

• 出版日期2014-5