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

Aram L. Karakhanyan, Martin H. Strömqvist
2014 Communications in Partial Differential Equations  
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
more » ... t of quasi-uniform convergence. As an application we obtain Poincaré's inequality for perforated domains.
doi:10.1080/03605302.2014.895013 fatcat:4h7wwxu7ubg2dlm5bak6qtuppi