Homogenization of highly oscillating boundaries with strongly contrasting diffusivity

We consider a linear diffusion problem, with strongly contrasting diffusivity, in a medium having a highly oscillating boundary. The problem is characterized by two small positive parameters: a parameter ε describing the periodicity of the oscillating boundary and a parameter a(ε) describing the contrasting diffusivity. As ε and a(ε) vanish, we pinpoint three different limit regimes depending on ratio l = lim α(ε)/ε e , according to l = 0, 0 < l < +∞, or l = +∞. In particular, the limit problem is nonlocal when 0 < l < +∞. We also prove corrector results.