Kostantinos Zemas: Homogenization of nonlinear randomly perforated materials

Full titel: Homogenization of nonlinear randomly perforated materials under minimal assumptions on the geometry

In this work we combine and generalize earlier works of Giunti-Höfer-Velazquez (on the homogenization of the Poisson equation in random critically perforated domains) and Ansini-Braides (on a variational approach for the more general nonlinear vectorial problem in the periodic setting), each one in the direction of the other.
Namely, we show that under similar general assumptions on the geometry of the random perforations as the ones posed in the work of Giunti, Höfer and Velazquez, the stochastic analogue of the result of Ansini-Braides holds true, with an average deterministic nonlinear capacitary-term appearing in the Γ-limit.
This is joint work with Caterina Zeppieri and Lucia Scardia.