Boundary condition for Ginzburg-Landau theory of superconducting layers

Electrostatic charging changes the critical temperature of superconducting thin layers. To understand the basic mechanism, it is possible to use the Ginzburg-Landau theory with the boundary condition derived by de Gennes from the BCS theory. Here we show that a similar boundary condition can be obtained from the principle of minimum free energy.
We compare the two boundary conditions and use the Budd-Vannimenus theorem as a test of approximations.