Published Paper
Inserted: 14 dec 2001
Journal: J. Funct. Anal.
Volume: 186
Number: 2
Pages: 432-520
Year: 2001
Abstract:
Let $\Omega$ be a bounded, simply connected, regular domain of
$R^N$, $N\ge 2$. For $0<\varepsilon<1$, let $u_\varepsilon :\Omega\to C$
be a smooth solution of the Ginzburg-Landau equation in $\Omega$ with
Dirichlet boundary condition $g_\varepsilon$, i.e.,
$$ \cases{ -\Delta
u\varepsilon ={1\over \varepsilon2} u\varepsilon (1-
u\varepsilon
2) & {\rm in } \Omega,\cr
u\varepsilon= g\varepsilon & {\rm on } \partial\Omega. \cr}
$$
We are interested in the asymptotic behavior
of $u_\varepsilon$ as $\varepsilon$ goes to zero under the assumption that
$E_\varepsilon(u_\varepsilon)\le M_0
\log\varepsilon
$ and some conditions on $g_\varepsilon$
which allow singularities of dimension $N-3$ on $\partial\Omega$.
Keywords: Ginzburg-Landau equation
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