On Sensitive Vector Poisson and Stokes Problems
Jean‐Luc Guermond, Luigi Quartapelle · Mathematical Models and Methods in Applied Sciences · 1997
Lions/Sanchez-Palencia's theory of sensitive boundary value problems is extended from the scalar biharmonic equation to the vector Poisson equation and the Stokes problem associated with the bilinear form (∇ × u, ∇ × v) + (∇ · u, ∇ · v). For both problems the specification of completely natural conditions for the vector unknown on a part of the boundary leads to a variational formulation admitting a unique solution which is however sensitive to abitrarily small smooth perturbations of the data, as shown in the present paper.