Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the maximum principles and the quantitative version of the Hopf lemma
  for uniformly elliptic integro-differential operators   In the present paper we prove estimates on {subsolutions of the equation
$-Av+c(x)v=0$}, $x\in D$, where $D\subset \bbR^d$ is a domain (i.e. an open and
connected set) and $A$ is an integro-differential operator of the Waldenfels
type, whose differential part satisfies the uniform ellipticity condition on
compact sets. In general, the coefficients of the operator need not be
continuous but only bounded and Borel measurable. Some of our results may be
considered "quantitative" versions of the Hopf lemma, as they provide the lower
bound on the outward normal directional derivative at the maximum point of a
subsolution %on a boundary of a domain in terms of its value at the point. We
shall also show lower bounds on the subsolution around its maximum point by the
principal eigenfunction associated with $A$ and the domain. Additional results,
among them the weak and strong maximum principles, the weak Harnack inequality
are also proven.

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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
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The categories of this paper are: econ
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th