Enhanced superconductivity at a corner for the linear BCS equation

Abstract We consider the critical temperature for superconductivity, defined via the linear BCS equation. We prove that at weak coupling the critical temperature for a sample confined to a quadrant in two dimensions is strictly larger than the one for a half-space, which in turn is strictly larger than the one for $\mathbb {R}^2$ . Furthermore, we prove that the relative difference of the critical temperatures vanishes in the weak coupling limit.