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

TL;DR

This paper studies the homogenization of the p-Laplace equation with periodic coefficients affected by a local defect, extending previous linear results to nonlinear cases with p > 2, and establishing convergence under certain conditions.

Contribution

It extends homogenization results for the p-Laplace equation with local defects from linear to nonlinear cases for p > 2, including corrector construction and convergence analysis.

Findings

Constructed correctors for the nonlinear p-Laplace equation.

Proved convergence to the homogenized solution under non-degeneracy assumptions.

Extended homogenization theory to nonlinear, defect-perturbed settings.

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.