  We consider a gas of fermions at zero temperature and low density,
interacting via a microscopic two body potential which admits a bound state.
The particles are confined to a domain with Dirichlet (i.e. zero) boundary
conditions. Starting from the microscopic BCS theory, we derive an effective
macroscopic Gross-Pitaevskii (GP) theory describing the condensate of fermion
pairs. The GP theory also has Dirichlet boundary conditions.
  Along the way, we prove that the GP energy, defined with Dirichlet boundary
conditions on a bounded Lipschitz domain, is continuous under interior and
exterior approximations of that domain.
