Homogenization of quasilinear problems with semilinear terms and Signorini boundary conditions in perforated domains

Abstract

This paper studies the upscaling of an elliptic problem with a highly oscillating quasilinear matrix coefficient, a quasilinear term, and a semilinear term in domains periodically perforated with holes of critical size. A Signorini boundary condition is imposed on the boundary of the holes, while a Dirichlet boundary condition is prescribed on the exterior boundary. Using the periodic unfolding method, we obtain an obstacle problem with a nonnegativity spreading effect.