Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal constants in nontrapping resolvent estimates and applications in
  numerical analysis   We study the resolvent for nontrapping obstacles on manifolds with Euclidean
ends. It is well known that for such manifolds, the outgoing resolvent
satisfies $\|\chi R(k) \chi\|_{L^2\to L^2}\leq C{k}^{-1}$ for ${k}>1$, but the
constant $C$ has been little studied. We show that, for high frequencies, the
constant is bounded above by $2/\pi$ times the length of the longest
generalized bicharacteristic of $|\xi|_g^2-1$ remaining in the support of
$\chi.$ We show that this estimate is optimal in the case of manifolds without
boundary. We then explore the implications of this result for the numerical
analysis of the Helmholtz equation.

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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
16
The categories of this paper are: stat
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The categories of this paper are: nlin
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol