Abstract
We study the BCS critical temperature on half-spaces in dimensions d = 1, 2, 3 with Dirichlet or Neumann boundary conditions. We prove that the critical temperature on a half-space is strictly higher than on Rd , at least at weak coupling in d = 1, 2 and weak coupling and small chemical potential in d = 3 . Furthermore, we show that the relative shift in critical temperature vanishes in the weak coupling limit.