Jerrard, Robert L.; Soner, Halil Mete The Jacobian and the Ginzburg-Landau energy. (English) Zbl 1034.35025 Calc. Var. Partial Differ. Equ. 14, No. 2, 151-191 (2002). 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. Reviewer: Vicenţiu D. Rădulescu (Craiova) Cited in 97 Documents 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 Keywords:Ginzburg-Landau energy; minimization problem; asymptotic analysis PDF BibTeX XML Cite \textit{R. L. Jerrard} and \textit{H. M. Soner}, Calc. Var. Partial Differ. Equ. 14, No. 2, 151--191 (2002; Zbl 1034.35025) Full Text: DOI OpenURL