Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gevrey local solvability in locally integrable structures   We consider a locally integrable real-analytic structure, and we investigate
the local solvability in the category of Gevrey functions and
ultradistributions of the complex d' naturally induced by the de Rham complex.
We prove that the so-called condition Y(q) on the signature of the Levi form,
for local solvability of d' u=f, is still necessary even if we take f in the
classes of Gevrey functions and look for solutions u in the corresponding
spaces of ultradistributions.

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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th