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Surface nucleation of superconductivity in 3-dimensions. (English) Zbl 0972.35152
The authors study the surface nucleation of superconductivity and estimate the value of the upper critical field $$H_{C_3}$$ for superconductors occupying an arbitrary smooth domain in $$\mathbb{R}^3$$. It is proved that $$H_{C_3}\simeq K/\beta_0$$, the ratio of the Ginzburg-Landau parameter $$K$$ and the first eigenvalue $$\beta_0$$ for the Schrödinger operator with unit magnetic field on the half plane. When the applied magnetic field is spatially 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 nonhomogeneous applied fields is also discussed.

##### MSC:
 35Q55 NLS equations (nonlinear Schrödinger equations) 82D55 Statistical mechanical studies of superconductors
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##### References:
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