On the Laplacean transfer across fractal mixtures (Q2852329)

Reinforcement problems in domains with a fractal boundary are considered via homogenization approach. The fractal layer is approximated by insulating layers with both thickness and conductivity of the fibre tending to zero. It is shown that the asymptotic behavior of the solutions \(u(n)\) of the Dirichlet problem for elliptic operators depends on the conductivity parameters, and the sequence \(u(n)\) converges to the variational solution of the Robin problem, the Neumann problem or the Dirichlet problem on the simply connected domain (whose boundary is a fractal curve) depending on the behavior of the conductivity parameters \(c(n)\). Convergence of the spectral structures associated with the operators is also discussed. M-convergence of the functionals corresponding to the reinforcement problem is proved.