Calculus of Variations and Geometric Measure Theory

A. Cosenza - M. Goldman - A. Zilio

A $Γ$-convergence result for 2D type-I superconductors

created by cosenza on 29 Apr 2025
modified on 11 Nov 2026

[BibTeX]

Accepted Paper
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Inserted: 29 apr 2025
Last Updated: 11 nov 2026

Journal: Interfaces and Free Boundaries
Year: 2025

ArXiv: 2504.19587 PDF

Abstract:

We consider a 2D non-standard Modica-Mortola type functional. This functional arises from the Ginzburg-Landau theory of type-I superconductors in the case of an infinitely long sample and in the regime of comparable penetration and coherence lengthes. We prove that the functional $\Gamma$-converges to the perimeter functional. This result is a first step in understanding how to extend the results of Conti, Goldman, Otto, Serfaty (2018) to the regime of non vanishing Ginzburg-Landau parameter $\kappa$.