Periodic homogenization for quasi-filling fractal layers

In this paper, we study the periodic homogenization of the stationary heat equation in a domain with two connected components, separated by an oscillating interface defined on prefractal Koch type curves. The problem depends both on the parameter n, which is the index of the prefractal iteration, and ε, that defines the periodic structure of the composite material. First, we study the limit as n goes to infinity, giving rise to a limit problem defined on a domain with fractal interface. Then, we compute the limit as ε vanishes, showing that the homogenized problem is strictly dependent on the amplitude of the oscillations and the parameter appearing in the transmission condition. Finally, we discuss about the commutative nature of the limits in ε and n.