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Equilibrium configurations of crystals. (English) Zbl 0673.73012
The aim of the paper is to determine equilibrium configurations of elastic crystals under displacement loding conditions by using direct methods. It is proved that for homogeneous deformation the minimum energy configuration is determined by the subenergy density of the energy density W. The results are extended for more general boundary conditions and also for some special homogeneous configurations admitting parametrized measure minima. Stable parametrized measure minimizers are introduced and also parametrized measures which minimize energy with respect to small compactly supported perturbations are studied for which the rank-one convexity of W is proved.
Reviewer: V.Tigoiu

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74E10 Anisotropy in solid mechanics
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
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