Asymptotic behavior of minimizers of a Ginzburg–Landau equation with weight near their zeroes
Anne Beaulieu, Rejeb Hadiji · Asymptotic Analysis · 2000
Introduction. Let G be a smooth bounded domain in R 2 and p a smooth positive bounded map from G into R. For a given map g 2 C 1 (@G; S 1 ) such that deg(g; @G) = d ? 0, we consider the problem (1:1) min u2H 1 g (G;C) E " (u) where E " is the Ginzburg-Landau type functional (1:2) E " (u) = 1 2 Z G p j ru j 2 + 1 4" 2 Z G p(1\\Gamma j u j 2 ) 2 and H 1 g