  We consider the linear BCS equation, determining the BCS critical
temperature, in the presence of a boundary, where Dirichlet boundary conditions
are imposed. In the one-dimensional case with point interactions, we prove that
the critical temperature is strictly larger than the bulk value, at least at
weak coupling. In particular, the Cooper-pair wave function localizes near the
boundary, an effect that cannot be modeled by effective Neumann boundary
conditions on the order parameter as often imposed in Ginzburg-Landau theory.
We also show that the relative shift in critical temperature vanishes if the
coupling constant either goes to zero or to infinity.
