Two-scale convergence of a class of r-forms: rewriting of periodic homogenization of Maxwell’s equations

Periodic homogenization is studied for Maxwell’s equations with the linear conductivity. After generalizing the sequential compactness theorem of Nguetseng (SIAM J Math Anal 20:608–623, 1989), repeated to a sequence of r-differential forms of \(L^{1}\) $L^1$ -coefficients defined on an open set \(\Omega \) $\mathrm{\Omega }$ of \({\mathbb {R}}^N\) ${\mathbb{R}}^N$ with \(r \in \{ 0, 1, \ldots , N \},\) $r\in \{0,1,\dots ,N\},$ it is shown that the sequence of solutions to a class of reduced system converges to the solution of a homogenized reduced Maxwell’s equations.