Calculus of Variations and Geometric Measure Theory

N. Ansini - G. Dal Maso - C. I. Zeppieri

$\Gamma$-convergence and $H$-convergence of linear elliptic operators

created by zeppieri on 04 Mar 2012
modified on 14 Feb 2013


Published Paper

Inserted: 4 mar 2012
Last Updated: 14 feb 2013

Journal: J. Math. Pures Appl.
Volume: 99
Number: 3
Pages: 321--329
Year: 2013


We consider a sequence of linear Dirichlet problems $-{\rm div} ( \sigma_\varepsilon \nabla u_\varepsilon) = f$, with $u_\varepsilon \in H^1_0(\Omega)$ and $(\sigma_\varepsilon)$ uniformly elliptic and possibly non-symmetric. Using purely variational arguments we give an alternative proof of the compactness of $H$-convergence, originally proved by Murat and Tartar.

Keywords: $\Gamma$-convergence, linear elliptic operators, $H$-convergence