Limiting Behavior of the Ginzburg–Landau Functional☆

@inproceedings{Jerrard2002LimitingBO,
  title={Limiting Behavior of the Ginzburg–Landau Functional☆},
  author={Robert L. Jerrard and Halil Mete Soner},
  year={2002}
}
We continue our study of the functional Ee(u)≔∫U12∣∇u∣2+14e2(1−∣u∣2)2dx, for u∈H1(U;R2), where U is a bounded, open subset of R2. Compactness results for the scaled Jacobian of ue are proved under the assumption that Ee(ue) is bounded uniformly by a function of e. In addition, the Gamma limit of Ee(ue)/(ln e)2 is shown to be E(v)≔12∥v∥22+∥∇×v∥M, where v is the limit of j(ue)/∣ln e∣, j(ue)≔ue×Due, and ∥·∥M is the total variation of a Radon measure. These results are applied to the Ginzburg… CONTINUE READING

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