A basic homogenization problem for the $p$-Laplacian in ${\mathbb{R}}^d$ perforated along a sphere: $L^{\infty }$ estimates

Peter V. Gordon, Fedor Nazarov, Yuval Peres

We consider a boundary value problem for the $p$-Laplacian, posed in the exterior of small cavities that all have the same $p$-capacity and are anchored to the unit sphere in $\mat…