Calculus of Variations and Geometric Measure Theory

N. Ansini - O. Iosifescu

Approximation of anisotropic perimeter functionals by homogenization

created on 06 May 2004
modified by ansini on 17 Feb 2010


Published Paper

Inserted: 6 may 2004
Last Updated: 17 feb 2010

Journal: Boll. Un. Mat. Ital.
Volume: 3
Pages: 149-168
Year: 2010


We show that all anisotropic perimeter functionals of the form $ \int_{\partial^* E\cap\Omega} \varphi (\nu_E) \, d{\cal 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 $\int_{\partial^* E\cap \Omega} a(x/\epsilon) d{\cal H}^{n-1}$ ($a$ periodic).