Homogenization of a Dirichlet semilinear elliptic problem with a strong singularity at \(u=0\) in a domain with many small holes (Q1694695)

The topic considered here involves two kinds of difficulties: First of all, it is about the averaging (homogenization) of a semilinear elliptic equation posed in a domain with small holes -- so the asymptotics work must involve boundary-layer type arguments. The second difficulty refers to the singularity at \(u=0\) of the production term in the PDE (the right-hand side), which requires the introduction of a particular concept of solution. As main result, the authors perform rigorously the homogenization limit and discover the structure of the effective equations.