Original article

Calculus of Variations and Partial Differential Equations

, Volume 14, Issue 4, pp 447-482

First online:

Upper critical field for superconductors with edges and corners

  • Xing-Bin PanAffiliated withCenter for Mathematical Sciences, Zhejiang University, Hangzhou 310027, P.R. China

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The effect of non-smoothness of sample surfaces on the value of the upper critical field \(H_{C_3}\) and on the location of superconductivity nucleation is discussed. It is shown that, superconducting samples with edges and corners have higher value of \(H_{C_3}\) comparing to samples with smooth surfaces. Superconductivity nucleates first at the top and bottom edges in a cylinder with a finite height, and nucleates first at vertices in a cuboid.

Mathematics Subject Classification (1991): 35Q55, 81Q10, 82D55.