ON SENSITIVE VECTOR POISSON AND STOKES PROBLEMS

Lions/Sanchez-Palencia's theory of sensitive boundary value problems i s extended from the scalar biharmonic equation to the vector Poisson e quation and the Stokes problem associated with the bilinear form (del xu,del Xv)+(del.u, del.v). For both problems the specification of comp letely natural conditions for the vector unknown on a part of the boun dary leads to a variational formulation admitting a unique solution wh ich is however sensitive to abitrarily small smooth perturbations of t he data, as shown in the present paper.