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Fourth order moments of nonnegative measures on S² and applications
journal contributionposted on 1994-01-01, 00:00 authored by Gilles Francfort, Franc╠ºois Murat, Luc Tartar
Abstract: "We characterize the set of fourth order moments of a nonnegative measure on S┬▓. This question is motivated by problems of homogenization in linearized elasticity. As a consequence the minimum number of layering directions for generating general anisotropic, transversely isotropic or isotropic multilayered media is found. A key ingredient is a result about the decomposition of some nonnegative polynomials into sums of squares of polynomials; this particular result is due to Hilbert (1888)."