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In this paper we study the surface nucleation of superconductivity and estimate the value of the upper critical field H C 3 for superconductors occupying arbitrary bounded smooth domains in R 3 . We show that H C 3 & }Â; 0 , the ratio of the Ginzburg Landau parameter } and the first eigenvalue ; 0 of the Schro dinger operator with unit magnetic field on the half plane. When the applied magnetic field is spacially homogeneous and close to H C 3 , a superconducting layer nucleates on a portion of the surface at which the applied field is tangential to the surface. Nucleation under non-homogeneous applied fields is also discussed. 2000Academic Press

A remark on the dimension of the attractor for the Dirichlet problem of the complex Ginzburg-Landau equationIn this paper we study the eigenvalue problems for the Ginzburg-Landau operator with a large parameter in bounded domains in R 2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.

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