In this presentation, we discuss the homogenization of quasilinear elliptic problems with a jump on the interface between the two components proportional to the flux depending on a real parameter $\gamma$. The data is presumed to be an $L^1$ function and consequently, we consider the notion of renormalized solutions.

In the homogenization process, we employ the periodic unfolding method. The homogenized problem was afterwards identified to be a quasilinear elliptic problem with $L^1$ data for the case that the parameter $\gamma$ is less than $-1$.