Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $W^{2,1}$ regularity for solutions of the Monge-Amp\`ere equation   In this paper we prove that a strictly convex Alexandrov solution u of the
Monge-Amp\`ere equation, with right hand side bounded away from zero and
infinity, is $W_{\rm loc}^{2,1}$. This is obtained by showing higher
integrability a-priori estimates for $D^2 u$, namely $D^2 u \in L\log^k L$ for
any $k\in \mathbb N$.

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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex