## Abstract

We continue our study of the functional for u ε H^{1} (U; ℝ^{2}), where U is a bounded, open subset of ℝ^{2}. Compactness results for the scaled Jacobian of u^{e} are proved under the assumption that E_{e}(u^{e}) is bounded uniformly by a function of e. In addition, the Gamma limit of E_{e}(u^{e})/(ln e)^{2} is shown to be where v is the limit of j(u^{e})/ ln e , j(u^{e}) := u^{e} x Du^{e}, and ∥ · ∥_{ }is the total variation of a Radon measure. These results are applied to the Ginzburg-Landau functional with external magnetic field h_{ext} ≈ H ln e . The Gamma limit of F_{e}/(ln e)^{2} is calculated to be where v is as before, and a is the limit of A^{e}/ ln e .

Original language | English (US) |
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Pages (from-to) | 524-561 |

Number of pages | 38 |

Journal | Journal of Functional Analysis |

Volume | 192 |

Issue number | 2 |

DOIs | |

State | Published - Jul 10 2002 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Analysis

## Keywords

- BnV
- Compactness
- Gamma limit
- Ginzburg-Landau functional