Approximation of Anisotropic Perimeter Functionals by Homogenization

Ansini, N. ; Iosifescu, O.

Bollettino dell'Unione Matematica Italiana, Tome 3 (2010), p. 149-168 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

We show that all anisotropic perimeter functionals of the form $\int_{\partial^{\star}E \cap \Omega} \varphi(\nu_{E}) \, d\mathcal{H}^{n-1}$ ($\varphi$ convex and positively homogeneous of degree one) can be approximated in the sense of $\Gamma$-convergence by (limits of) isotropic but inhomogeneous perimeter functionals of the form $\int_{\partial^{\star}E \cap \Omega} a(x/\epsilon) \, d\mathcal{H}^{n-1}$ ($a$ periodic).

Détail

Publié le : 2010-02-01

MR 2605917 | Zbl 1196.49032

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