Calculus of Variations and Geometric Measure Theory

S. Conti - M. Goldman - F. Otto - S. Serfaty

A branched transport limit of the Ginzburg-Landau functional

created by goldman on 05 Apr 2017
modified on 20 Jun 2018


Accepted Paper

Inserted: 5 apr 2017
Last Updated: 20 jun 2018

Journal: J. Ecole Polytechnique
Year: 2017


We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional. We derive the simplified functional from the full Ginzburg-Landau model rigorously via $\Gamma$-convergence. The detailed analysis of the limiting procedure and the study of the limiting functional lead to a precise understanding of the multiple scales contained in the model.