This contribution is concerned with the formulation and mathematical investigation of a model for small elastic deformations which arises from multiplicative theories of elasto-plasticity, In a natural way it leads to a linear elliptic system with nonconstant coefficients for the deformation u. In contrast to infinitesimal plasticity the model should be valid for both large plastic deformations F-p and large deformation gradients F. The arising linear partial differential system is proved to have unique solutions by means of a generalized Kern's inequality. [References: 4]
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