Application of Uniform Distribution to Homogenization of a Thin Obstacle Problem withp − Laplacian

In this paper we study the homogenization of p − Laplacian with thin obstacle in a perforated domain. The obstacle is defined on the intersection between a hyperplane and a periodic perforation. We construct the family of correctors for this problem and show that the solutions for the ϵ −problem converge to a solution of a minimization problem of similar form but with an extra term involving the mean capacity of the obstacle. The novelty of our approach is based on the employment of quasi-uniform convergence. As an application we obtain Poincaré's inequality for perforated domains.