Titlebook: Vortices in the Magnetic Ginzburg-Landau Model; Etienne Sandier,Sylvia Serfaty Textbook 2007 Birkh�user Boston 2007 functions of complex v

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The Case of a Bounded Number of Vortices, number of vortices .. These estimates will be useful in the next chapter. The fact that the number of vortices is bounded independently of . allows us to obtain much more precise information with specific techniques: the upper and lower bounds will match up to an error which is .(1) as . → 0.

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Branches of Solutions,bounded and . unbounded, but not too large, in a wide regime of applied fields. These solutions are obtained by minimizing the energy . over subsets . of the functional space which correspond, very roughly speaking, to configurations with . vortices (or only allow for such when minimizing); the hear

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Asymptotics for Solutions, functional. We now wish to derive a criticality condition for a limiting vorticity measure associated to a family (.,.). of solutions of the Ginzburg-Landau system (.) which are not necessarily minimizing.

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1421-1750 ith results and current research.Acts a guide to the variousMore than ten years have passed since the book of F. Bethuel, H. Brezis and F. H´ elein, which contributed largely to turning Ginzburg–Landau equations from a renowned physics model into a large PDE research ?eld, with an ever-increasing nu

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First Properties of Solutions to the Ginzburg-Landau Equations,s, the material of the last two sections is more advanced, contains several results stated without proofs, and is only used in Chapter 5 and then Chapters 10 to 12. However, we feel that the material is important enough, like the uniqueness result of P. Mironescu (Theorem 3.2), or basic enough to deserve to be stated early on.

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