Abstract: The main goal of this paper is a compactness result for families of functions in the space (Special functions of Bounded Variation) defined on periodically perforated domains.

Our analysis avoids the use of any extension procedure in , weakens the hypothesis on the reference perforation to minimal ones and simplifies the proof of the results recently obtained in Refs 18, 14. Among the arguments we introduce, we provide a localized version of the Poincaré-Wirtinger inequality in .

As an application we study the asymptotic behavior of a variational model for brittle porous materials.

Finally, we slightly extend the well known homogenization theorem for Sobolev energies on perforated domains.

The main goal of this paper is a compactness result for families of functions in the space (Special functions of Bounded Variation) defined on periodically perforated domains.

Our analysis avoids the use of any extension procedure in , weakens the hypothesis on the reference perforation to minimal ones and simplifies the proof of the results recently obtained in Refs 18, 14. Among the arguments we introduce, we provide a localized version of the Poincaré-Wirtinger inequality in .

As an application we study the asymptotic behavior of a variational model for brittle porous materials.

Finally, we slightly extend the well known homogenization theorem for Sobolev energies on perforated domains.

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