Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Remark on the Helmholtz decomposition in domains with noncompact
  boundary   Let $\Omega$ be a domain with noncompact boundary. It is known that the
Helmholtz decomposition is not always valid in $L^p(\Omega)$ except for the
energy space $L^2 (\Omega)$. In this paper we consider a typical unbounded
domain whose boundary is given as a Lipschitz graph, and show that the
Helmholtz decomposition holds in certain anisotropic spaces which include some
infinite energy vector fields.

4
The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
26
The categories of this paper are: bayes-an