Local Minimizers of the Magnetic Ginzburg–Landau Functional with $S^1$-valued Order Parameter on the Boundary

V. Rybalko

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv, 61103, Ukraine

Abstract: It was shown in [L. Berlyand and V. Rybalko, Solution with Vortices of a Semi-Stiff Boundary Value Problem for the Ginzburg–Landau Equation, J. Eur. Math. Soc. 12 (2010), 1497–1531] that in doubly connected domains there exist local minimizers of the simplified Ginzburg–Landau functional with modulus one and prescribed degrees on the boundary, unlike global minimizers that typically do not exist. We generalize the results and techniques of the aforementioned paper to the case of the magnetic Ginzburg–Landau functional.

Key words and phrases: superconductivity, Ginzburg–Landau functional, variational problems with lack of compactness.

MSC: 35A01, 35J20, 35Q56

Received: 15.02.2013
Revised: 17.07.2013

Language: English

DOI: 10.15407/mag10.01.134

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