The density of superconductivity in domains with corners

Abstract

We compute the $L^2$-norm of the minimizer of the Ginzburg-Landau functional in a planar domain with a finite number of corners. Our computations are valid for a uniform applied magnetic field, large Ginzburg-Landau parameter and in the regime where superconductivity is confined near the corners of the domain.

References in corpus (3)

• Superconductivity in domains with corners
• Surface Superconductivity in Presence of Corners
• Strong diamagnetism for general domains and applications

Cited by in corpus (7)

• The breakdown of superconductivity in the presence of magnetic steps
• Magnetic steps on the threshold of the normal state
• Surface Effects in Superconductors with Corners
• Effects of Corners in Surface Superconductivity
• On the Ginzburg-Landau Energy of Corners
• Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)
• Almost Flat Angles in Surface Superconductivity