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Existence of the Ginzburg-Landau vortex number. (English) Zbl 0976.58012

Summary: The existence of the Ginzburg-Landau vortex number is established for any configuration with finite action. As a consequence, Bogomol’nyi’s formula for the critical action is valid for any finite action configuration.

MSC:

58E15 Variational problems concerning extremal problems in several variables; Yang-Mills functionals
35Q40 PDEs in connection with quantum mechanics
81T99 Quantum field theory; related classical field theories
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