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

Lin, Tai-Chia; Wang, Lihe

Methods Appl. Anal. 10, No. 1, 81-96 (2003).

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 \(\delta\).

MSC:

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