New formulations of linearized elasticity problems, based on extensions of Donati's theorem

The classical Donati theorem is used for characterizing smooth matrix fields as linearized strain tensor fields. In this Note, we give several generalizations of this theorem, notably to matrix fields whose components are only in H^-1. We then show that our extensions of Donati's theorem allow to reformulate in a novel fashion linearized three-dimensional elasticity problems as quadratic minimization problems with the strains as the primary unknowns. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). © 2006 Académie des sciences.