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arXiv · 2504.19587

A $\Gamma$-convergence result for 2D type-I superconductors

Alessandro Cosenza·Michael Goldman·Alessandro Zilio
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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 $\kappa$.

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Alessandro Cosenza, Michael Goldman, Alessandro Zilio. 2025-04-28. A $\Gamma$-convergence result for 2D type-I superconductors. https://arxiv.org/abs/2504.19587

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