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

Jerrard, Robert L.; Soner, Halil Mete

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)

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