Asymptotic analysis of non-symmetric linear operators via Gamma-convergence

We study the asymptotic behavior of a sequence of Dirichlet problems for second order linear operators in divergence form where the matrices are uniformly elliptic and possibly non symmetric. On account of the variational principle of Chercaev and Gibiansky, we are able to prove a variational characterization of the H-convergence of the sequence of matrices in terms of the Gamma-convergence of suitably associated quadratic forms.