Methods and Applications of Analysis

Volume 10 (2003)

Number 1

Regularity of the Minimizer for the D-Wave Ginzburg-Landau Energy

Pages: 81 – 96

DOI: https://dx.doi.org/10.4310/MAA.2003.v10.n1.a5

Authors

Tai-Chia Lin

Lihe Wang

Abstract

We study the minimizer of the d-wave Ginzburg-Landau energy in a specific class of functions. We show that the minimizer having distinct degree-one vortices is Holder continuous. Away from vortex cores, the minimizer converges uniformly to a canonical harmonic map. For a single vortex in the vortex core, we obtain the C^1/2-norm estimate of the fourfold symmetric vortex solution. Furthermore, we prove the convergence of the fourfold symmetric vortex solution under different scales of DELTA.

Published 1 January 2003