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

S. E. Pastukhova

Sbornik. Mathematics, Tome 192 (2001) no. 2, pp. 245-260

Résumé

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.

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