Dr. Jake Avila “Homogenization in Domains with Very Small Inclusions”

This work aims to describe the asymptotic behavior of an elliptic
boundary value problem with oscillating coefficients posed in a domain
in R^N for N ≥ 3 with very small inclusions and an imperfect interface.
On the interface, we prescribe the continuity of the conormal
derivatives and a jump of the solution proportional to ε^γ for γ ≤ 1;
while a Dirichlet condition is imposed on the outer boundary. In order
to homogenize the problem, we construct an extension of the periodic
unfolding method suitable for the geometry of the domain and we also prove some corrector results.
This is joint work with Bituin Cabarrubias.