Homogenization of a mixed problem with Signorini condition for an elliptic operator in a perforated domain

For the case of a 2-connected $\varepsilon$-periodic $(\varepsilon\in(0,1))$ perforated space with a bounded domain $\Omega_\varepsilon$ selected in it the homogenization property as $\varepsilon\to0$ is proved for the boundary-value problem for a second-order elliptic operator in the domain $\Omega_\varepsilon$ with one-sided condition of Signorini type on the boundaries of “cavities” and with Dirichlet condition on the outer boundary.