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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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