JournalsifbVol. 11 , No. 1DOI 10.4171/ifb/206

Regularity and nonexistence results for some free-interface problems related to Ginzburg–Landau vortices

  • Nam Q. Le

    New York University, United States
Regularity and nonexistence results for some free-interface problems related to Ginzburg–Landau vortices cover

Abstract

We study regularity and nonexistence properties for some free-interface problems arising in the study of limiting vorticities associated to the Ginzburg-Landau equations with magnetic field in two dimensions. Our results imply in particular that if these limiting vorticities concentrate on a smooth closed curve then they have a distinguished sign; moreover, if the domain is thin then solutions of the Ginzburg-Landau equations cannot have a number of vortices much larger than the applied magnetic field.