Surface nucleation of superconductivity in 3-dimensions

In this paper we study the surface nucleation of superconductivity and esti mate the value of the upper critical field H-C3 for superconductors occupyi ng arbitrary bounded smooth domains in R-3. We show that H-C3 similar or eq ual to kappa/beta (0), the ratio of the Ginzburg-Landau parameter kappa and the first eigenvalue beta (0) of the Schrodinger operator with unit magnet ic field on the halfplane. When the applied magnetic field is spacially hom ogeneous and close to H-C3, a superconducting layer nucleates on a portion of the surface at which the applied field is tangential to the surface. Nuc leation under non-homogeneous applied fields is also discussed. (C) 2000 Ac ademic Press.