Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The conformal plate buckling equation   We study the conformal plate buckling equation (Laplace--Beltrami)^2 u =1,
where the L-B operator is for the metric g = e^{2u}g_0, with $g_0$ the standard
Euclidean metric on R^2. This conformal elliptic PDE of fourth order is
equivalent to the nonlinear system of elliptic PDEs of second order, Delta u
+K_g e^(2u)=0, Delta K_g + e^(2u)=0, with x in R^2, describing a conformally
flat surface with a Gauss curvature function K_g that is generated
self-consistently through the metric's conformal factor.

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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: q-alg