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The uniqueness of solutions of some variational problems of the theory of phase equilibrium in solid bodies

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Abstract

A variational problem in the theory of phase equilibrium is considered in a geometrically linear statement. A solid body is assumed to have two different phases with the same elasticity tensor. In the case of the Dirichlet condition, it is proved that under some restrictions on the elasticity tensor a solution of the relaxational variational problem is unique provided that the difference of the strain tensors relative to the zero stress state of the corresponding phase is anisotropic. Bibliography: 7 titles.

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Authors
  1. G. A. Seregin
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Additional information

Translated fromProblemy Matematicheskogo Analiza, No. 15, 1995, pp. 220–232.

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Seregin, G.A. The uniqueness of solutions of some variational problems of the theory of phase equilibrium in solid bodies. J Math Sci 80, 2333–2348 (1996). https://doi.org/10.1007/BF02362391

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  • DOI: https://doi.org/10.1007/BF02362391

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