On the Laplacean transfer across fractal mixtures

Skew Brownian Diffusions Across Koch Interfaces

“…In order to study the asymptotic behaviour of the functions u n , we fix the further assumptions We also introduce the following results which have been proved in [20] and turn out to be useful further on. .…”

“…Section 2 introduces notation and definitions of the pre-fractal and fractal Koch curves. Moreover, we recall the homogenization results obtained in [20]. Section 3 gives some basic aspects about positive continuous additive functionals and random times.…”

Fractional Equations Via Convergence of Forms

“…The previous example is given for a regular domain. A similar example can be given for domains with fractal boundaries as in [22] where the authors have obtained asymptotic results for skew Brownian diffusions across Koch interfaces by using M −convergence results proved in [20], [24], [25]. We recall that M −convergence results have been obtained on fractal structures in order to study several boundary value problems ( [2], [23], [56], [57], [58]), reinforcement problems for variational inequalities ( [26]), dynamical quasi-filling fractal layers, layered fractal fibers and potentials ( [27], [74], [75]).…”

Reinforcement problems for variational inequalities on fractal sets

“…The homogenization theory for domains with a fractal boundary have been developed in [26][27][28], and [29] for highly conductive layers and in [11,13], and [14] for insulating layers. We also wish to mention [4,15], where the reinforcement has a different structure.…”