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Estimates for the trace of an averaged tensor

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Abstract

We develop a variational method for deriving estimates for averaged tensors for operators of the theory of elasticity and fourth-order operators. In the special case of two-phase media our results imply the Hashin-Shtrikman “bound” known in the theory of elasticity. As an application of our results, we prove an analogue of the Polya-Shiffer theorem.

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Authors and Affiliations

  1. Vladimir Pedagogical Institute, USSR

    V. V. Zhikov

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  1. V. V. Zhikov
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 6, pp. 745–755, June, 1991.

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Zhikov, V.V. Estimates for the trace of an averaged tensor. Ukr Math J 43, 694–704 (1991). https://doi.org/10.1007/BF01058936

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  • DOI: https://doi.org/10.1007/BF01058936

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