A model describing small elastic deformations and Korn's inequality with nonconstant coefficients

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 he 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 Korn's inequality.