Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Caffarelli Alternative in Measure for the Nondivergence Form
  Elliptic Obstacle Problem with Principal Coefficients in VMO   We study the obstacle problem with an elliptic operator in nondivergence form
with principal coefficients in VMO. We develop all of the basic theory of
existence, uniqueness, optimal regularity, and nondegeneracy of the solutions.
These results, in turn, allow us to begin the study of the regularity of the
free boundary, and we show existence of blowup limits, a basic measure
stability result, and a measure-theoretic version of the Caffarelli alternative
proven in Caffarelli's 1977 paper "The regularity of free boundaries in higher
dimensions."

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The categories of this paper are: funct-an
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The categories of this paper are: cs
6
The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
9
The categories of this paper are: nlin