Stress concentration for closely located inclusions in nonlinear perfect conductivity problems

We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium $\mathrm{\Omega }?{\mathbb{R}}^N$, $N\ge 2$. The governing equation may be degenerate of p-Laplace type, with $1<p\le N$. We prove optimal $L^{\infty }$ estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero.