Well-posedness of mixed formulations in elasticity

Mixed formulations in elasticity are analysed and existence and uniqueness of the solution are discussed in the context of Hilbert space theory. New r esults, referred to in the analysis of elasticity problems, are proved. The y are concerned with the closedness of the product of two linear operators and a projection property equivalent to the closedness of the sum of two cl osed subspaces. A set of two necessary and sufficient conditions for the we ll-posedness of an elastic problem with a singular elastic compliance provi des the most general result of this kind in linear elasticity. Sufficient c riteria Sor the well-posedness of elastic problems in structural mechanics including the presence of supporting elastic beds are contributed and appli cations are exemplified.