Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mean Value Theorem and Basic Properties of the Obstacle Problem for
  Divergence Form Elliptic Operators   In 1963, Littman, Stampacchia, and Weinberger proved a mean value theorem for
elliptic operators in divergence form with bounded measurable coefficients. In
the Fermi lectures in 1998, Caffarelli stated a much simpler mean value theorem
for the same situation, but did not include the details of the proof. We show
all of the nontrivial details needed to prove the formula stated by Caffarelli,
and in the course of showing these details we establish some of the basic facts
about the obstacle problem for general elliptic divergence form operators, in
particular, we show a basic quadratic nondegeneracy property.

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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga