Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Periodic unfolding and homogenization for the Ginzburg-Landau Equation   We investigate, on a bounded domain $\Omega$ of $\R^2$ with fixed
$S^1$-valued boundary condition $g$ of degree $d>0$, the asymptotic behaviour
of solutions $u_{\varepsilon,\delta}$ of a class of Ginzburg-Landau equations
driven by two parameter : the usual Ginzburg-Landau parameter, denoted
$\varepsilon$, and the scale parameter $\delta$ of a geometry provided by a
field of $2\times 2$ positive definite matrices $x\to A(\frac{x}{\delta})$. The
field $\R^2\ni x\to A(x)$ is of class $W^{2,\infty}$ and periodic. We show, for
a suitable choice of the $\varepsilon$'s depending on $\delta$, the existence
of a limit configuration $u_\infty\in H^1_g(\Omega,S^1)$, which, out of a
finite set of singular points, is a weak solution of the equation of
$S^1$-valued harmonic functions for the geometry related to the usual
homogenized matrix $A^0$.

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The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys