Weakly singular Steklov condition in the multidimensional case

In an $n$-dimensional $(n>3)$ domain, we consider a Steklov-type problem with rapidly changing conditions (the Steklov condition alternates with the homogeneous Dirichlet condition). The coefficient in the Steklov condition is a rapidly oscillating function depending on a small parameter $\varepsilon$ and having the order $O(1)$ outside small spherical layer inclusions and the order $O((\varepsilon\delta)^{-m})$ inside them. These inclusions have an $O(\varepsilon\delta)$ diameter and lie at a distance of $O(\delta)$ from each other, where $\delta=\delta(\varepsilon)\to0$. In the case $m<2$ (weak singularity), the rate of convergence of solutions to the original problem as the small parameter tends to zero is estimated.