Author:
Correggi Michele,Giacomelli Emanuela L.
Abstract
AbstractWe study the Ginzburg–Landau functional describing an extreme type-II superconductor wire with cross section with finitely many corners at the boundary. We derive the ground state energy asymptotics up to o(1) errors in the surface superconductivity regime, i.e., between the second and third critical fields. We show that, compared to the case of smooth domains, each corner provides an additional contribution of order $$ {\mathcal {O}}(1) $$
O
(
1
)
depending on the corner opening angle. The corner energy is in turn obtained from an implicit model problem in an infinite wedge-like domain with fixed magnetic field. We also prove that such an auxiliary problem is well-posed and its ground state energy bounded and, finally, state a conjecture about its explicit dependence on the opening angle of the sector.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference55 articles.
1. Alouges, F., Bonnaillie-Nöel, V.: Numerical computations of fundamental eigenstates for the Schrödinger operator under constant magnetic field. Numer. Methods Partial Differ. Equ. 22, 1090–1105 (2006)
2. Abrikosov, A.: On the magnetic properties of superconductors of the second type. Sov. Phys. JETP 5, 1174–1182 (1957)
3. Adams, R.A.: Sobolev Spaces. Academic Press, Cambridge (1975)
4. Almog, Y., Helffer, B.: The distribution of surface superconductivity along the boundary: on a conjecture of X.B. Pan. SIAM J. Math. Anal. 38, 1715–1732 (2007)
5. Assaad, W.: The breakdown of superconductivity in the presence of magnetic steps. Commun. Contemp. Math. 23, 2050005 (2019)
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