Homogenization for the $p$-Laplacian in a $d$-dimensional ball perforated along the unit sphere: the critical case $p=d$

Peter V. Gordon, Yuval Peres

We study a boundary value problem for the $p$-Laplacian in the perforated domain $B(0,\rho )\setminus \Gamma \subset {\mathbb{R}}^d$, where $\rho >1$ and $\Gamma$ is the union of many small compact cavi…