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.


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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