Geodesic
Approximation of Anisotropic Perimeter Functionals by Homogenization
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 149-168

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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). 
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     author = {Ansini, N. and Iosifescu, O.},
     title = {Approximation of {Anisotropic} {Perimeter} {Functionals} by {Homogenization}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {149--168},
     publisher = {mathdoc},
     volume = {Ser. 9, 3},
     number = {1},
     year = {2010},
     zbl = {1196.49032},
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     url = {http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a6/}
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Ansini, N.; Iosifescu, O. Approximation of Anisotropic Perimeter Functionals by Homogenization. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 149-168. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a6/