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E. Reissner suggested a variational theorem for the theory of elasticity, related closely to the well-known Trefftz method. In the present paper, the Reissner's theorem is discussed within the range of linear anisotropic and non-homogeneous elasticity. For the traction boundary-value problem, the minimal property of the functional and the convergence of any minimizing sequence are proved. For the displacement boundary-value problem and sime mixed problems, it is shown that a modification is necessary. Then, in case of the displacement problem, the maximal property of the functional on the modified class of admissible functions and the convergence of maximizing sequence are proved.
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