Homogenization of the p--Laplace equation in a periodic setting with a local defect

Abstract

In this paper, we consider the homogenization of the p−Laplace equation with a periodic coefficient that is perturbed by a local defect. This setting has been introduced in [6, 7] in the linear setting p = 2. We construct the correctors and we derive convergence results to the homogenized solution in the case p > 2 under the assumption that the periodic correctors are non degenerate.

Defects in homogenization theory

“…The defects may also affect the geometry of the domain itself, as is the case for domains with nonperiodic arrays of perforations, a case studied in the works [23,48] by X. Blanc and S. Wolf.…”