Regularity of the minimizer for the \(d\)-wave Ginzburg-Landau energy. (English) Zbl 1129.35333

Summary: 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 Hölder 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 \(C^{\frac{1}{2}}\)-norm estimate of the fourfold symmetric vortex solution. Furthermore, we prove the convergence of the fourfold symmetric vortex solution under different scales of \(\delta\).


35J20 Variational methods for second-order elliptic equations
35B25 Singular perturbations in context of PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
49N60 Regularity of solutions in optimal control
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
82D55 Statistical mechanics of superconductors
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