论文信息 - The proofs of the optimal bounds for mixtures of two anisotropic conducting materials in two dimensions

The proofs of the optimal bounds for mixtures of two anisotropic conducting materials in two dimensions

Abstract We provide a complete proof of the result announced 20 years ago in Francfort and Murat [Francfort, G.A., Murat, F., 1987. Optimal bounds for conduction in two-dimensional, two-phase, anisotropic media. In: Knops, R.J., Lacey, A.A., (Eds.), Nonclassical Continuum Mechanics (Durham, 1986), London Mathematical Society Lecture Note Series, vol. 122, Cambridge University Press, Cambridge, pp. 197–212], 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 Francfort and Murat (1987)) of the sets of conducting materials with arbitrary orientation which are stable under H -convergence in two dimensions.

Gilles A. Francfort | François Murat

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