Homogenization of the Oscillating Dirichlet Boundary Condition in General Domains

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.

Version to appear in J. Math. Pures Appl. Added Remarks 1.2 and 1.7. Removed some extraneous statements of previous results (previously Corollaries 2.7 and 2.12). Changed the statement and proof of Lemma 3.1 to fix a small error and R^{-α} is now (N/R)^α here and in later uses of the Lemma. 23 pages

Cited by in corpus (2)

• Quantitative Homogenization of Elliptic PDE with Random Oscillatory Boundary Data
• On Homogenization Problems with Oscillating Dirichlet Conditions in Space-Time Domains