High-contrast homogenisation of linear PDEs

I will speak about a problem of homogenisation of a linear PDE with periodic coefficients. Coefficients of the operator are not supposed to be uniformly elliptic, they degenerate on a periodic subset of the domain as the period tends to zero (hence the term high-contrast homogenisation). The limit homogenised operator in this case is two-scale and possesses a band-gap spectrum. One of the key elements in the analysis of such type of problems is two-scale convergence (Nguetseng).