Convergence Rate of the Periodic Homogenization of Weighted p‐Laplace Equations for Various Kinds of Correctors

In this paper, we explore the convergence rate of the periodic homogenization of the weighted ‐Laplace equations with two different kinds of correctors. The results fill the gap for the case , where the convergence rate is not known yet. We reduce the problem of calculating the convergence rate to the layer and co‐layer estimates of the inhomogeneous ‐Laplace type equations. We concentrate on the case where the corrector is linear on by imposing a special condition on the weight, which simplifies the proof. At last, our results return to convergence rate when , which coincide with the previous results.