TY - JOUR
T1 - Ginzburg-Landau Vortices in Inhomogeneous Superconductors
AU - Huaiyu Jian  & Youde Wang 
JO - Journal of Partial Differential Equations
VL - 3
SP - 45
EP - 60
PY - 2002
DA - 2002/08
SN - 15
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5454.html
KW - Vortex
KW - Ginzburg-Landau equation
KW - elliptic estimate
KW - H¹-strong convergence
AB -  We study the vortex convergence for an inhomogeneous Ginzburg-Landau equation, -Δu = ∈^{-2}u(a(x) - |u|²), and prove that the vortices are attracted to the minimum point b of a(x) as ∈ → 0. Moreover, we show that there exists a subsequence ∈ → 0 such that u_∈ converges to u strongly in H¹_{loc}(\overline{Ω} \ {b}).