## The Jacobian and the Ginzburg-Landau energy.(English)Zbl 1034.35025

The paper deals with the study of the Ginzburg-Landau energy functional on a bounded, open subset of $$\mathbb{R}^2$$. The main result of the paper asserts that for any sequence of functions $$(u^\varepsilon)$$ with uniformly bounded Ginzburg-Landau energy, the corresponding sequence of Jacobians $$(Ju^\varepsilon)$$ is precompact in an appropriate topology. The authors also characterize all possible weak limits of the Jacobians and prove a $$\Gamma$$-limit result for the Ginzburg-Landau functional. The proofs are based on refined elliptic estimates combined with powerful topological arguments.

### MSC:

 35J50 Variational methods for elliptic systems 35Q80 Applications of PDE in areas other than physics (MSC2000) 49J35 Existence of solutions for minimax problems 82D55 Statistical mechanics of superconductors
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