Stress concentration for closely located inclusions in nonlinear perfect conductivity problems

Giulio Ciraolo, Angela Sciammetta

Published 2018-09-21Version 1

We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. 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.