We consider the energy functional of a two-phase elastic medium \documentclass[12pt]{minimal}
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$$I[u,\chi ,\mu ] = \int\limits_\Omega {\{ \chi (x)(F^ + (\nabla u(x)) + \mu ) + (1 - \chi (x))F^ - (\nabla u(x))\} } dx$$
\end{document} with quadratic energy densities \documentclass[12pt]{minimal}
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$$F^ \pm (M) = a_{ijkl}^ \pm (e(M) - \zeta ^ \pm )_{ij} (e(M) - \zeta ^ \pm )_{kl} $$
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$$u \in W_2^1 (\Omega ,R^m )$$
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$$u|_{\partial \Omega } = u_0 |_{\partial \Omega } ,{\text{ }}e(\nabla u_0 ) \equiv e_0 \ne e_0 (x)$$
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$$\chi $$
\end{document} is a measurable characteristic function. Under some natural conditions on the data of the problem, we prove the existence of an interval (t-,t+) of the change of temperature \documentclass[12pt]{minimal}
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$$\mu $$
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$$\hat \mu ,\hat \chi $$
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$$\hat \chi \equiv {\text{1}}$$
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$$\mu < t^ - $$
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$$\hat \mu ,\hat \chi $$
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$$\hat \chi \equiv 0{\text{ }}for{\text{ }}\mu >t^ + $$
\end{document}. The energy functional has no minimizers \documentclass[12pt]{minimal}
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$$\hat \mu ,\hat \chi $$
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$$\hat \chi \equiv 1$$
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$$\hat \chi \equiv 0$$
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$$\mu \in (t^ - ,t^ + )$$
\end{document}. We derive two-sided estimates for the numbers \documentclass[12pt]{minimal}
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$$t^ \pm $$
\end{document} in terms of the characteristics of the two-phase elastic medium and the boundary condition. Bibliography: 3 titles.