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The never before published complete proofs of the optimal bounds for the mixture of two anisotropic conducting materials in two dimensions

We provide a complete proof of the result announced twenty years ago in [5], namely the characterization in two dimensions of the set of the effective conductivities obtained by mixing two anisotropic conducting materials with arbitrary orientation. We also provide a complete proof of the characterization (also already announced in [5]) of the sets of conducting materials with arbitrary orientation which are stable under H-convergence in two dimensions.