QUANTITATIVE ANALYSIS OF BOUNDARY LAYERS IN PERIODIC HOMOGENIZATION

Scott Armstrong (1) , Tuomo Kuusi (2) , Jean-Christophe Mourrat (3) , Christophe Prange (4)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Department of Mathematics [Aalto]
3 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
4 IMB - Institut de Mathématiques de Bordeaux

We prove quantitative estimates on the rate of convergence for the oscillating Dirichlet problem in periodic homogenization of divergence-form uniformly elliptic systems. The estimates are optimal in dimensions larger than three and new in every dimension. We also prove a regularity estimate on the homogenized boundary condition.

Domaines: Equations aux dérivées partielles [math.AP]

Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat, Christophe Prange. QUANTITATIVE ANALYSIS OF BOUNDARY LAYERS IN PERIODIC HOMOGENIZATION. 2017. ⟨hal-01483483⟩