[en] The idea of the present paper is born from the reading of very interesting papers
of Amrouche, Ciarlet and Mardane [1, 2] concerning the equivalence of a lot of
properties related to Lions’ lemma. All these properties are intimately related
to Stokes’ problem in fluid mechanics, one of them being the LBB condition
of this problem. This led us to investigate the following question : are there
similar results in the abstract case of a general saddle point problem ? We
found that the answer is positive, and this is the object of the present paper.
After obtention of the abstract results, a final section of this paper is devoted
to Stokes’ problem, in order to demonstrate the power of the abstract theory.
