Abstract
In this paper we improve the estimate obtained by Lu–Pan on the value of the upper critical field HC3(κ) for a cylindrical superconductor with cross section Ω being an arbitrary 2-dimensional smooth bounded domain. We also show that, when a homogeneous magnetic field is applied along the axis of the cylinder with magnitude of the field close to HC3, superconductivity nucleates first at the surface of the sample where the curvature of ∂Ω is maximal.
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