*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

**Abstract:**

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

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