Electron. J. Diff. Eqns., Vol. 1999(1999), No. 30, pp. 1-21.

Radial minimizers of a Ginzburg-Landau functional

Yutian Lei, Zhuoqun Wu, & Hongjun Yuan

We consider the functional
$$ E_\varepsilon (u,G) ={1\over p} \int_G|\nabla u|^p
     +{1 \over 4\varepsilon^p} \int_G(1-|u|^2)^2 $$
with p greater than 2 and d positive, on the class of functions $W=\{u(x)=f(r)e^{id\theta} \in W^{1,p}(B,C);
      f(1)=1,f(r)\geq 0\}$. The location of the zeroes of the minimizer and its convergence as $\varepsilon$ approaches zero are established.

Submitted June 8, 1999. Published September 9, 1999.
Math Subject Classifications: 35J70
Key Words: Ginzburg-Landau functional, radial functional, zeros of a minimizer.

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Yutian Lei, Zhuoqun Wu, & Hongjun Yuan
Institute of Mathematics
Jilin University
130023 Changchun China
E-mail: wzq@mail.jlu.edu.cn
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