On the asymptotic behavior of elliptic problems in periodically perforated domains with mixed-type boundary conditions

Abstract

Using the periodic unfolding method, we analyze the asymptotic behavior of a class of elliptic equations with highly oscillating coefficients, in a perforated periodic domain. We consider, in each period, two types of holes and we impose, on their boundaries, different conditions of Neumann and/or Signorini types. The limit problems contain additional terms which capture both the influence of the size of the holes and the effect of the conditions imposed on their boundaries.