Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-scale method for the Monge-Amp\`ere Equation: Pointwise Error
  Estimates   In this paper we continue the analysis of the two-scale method for the
Monge-Amp\`ere equation for dimension $d \geq 2$ introduced in [10]. We prove
continuous dependence of discrete solutions on data that in turn hinges on a
discrete version of the Alexandroff estimate. They are both instrumental to
prove pointwise error estimates for classical solutions with H\"older and
Sobolev regularity. We also derive convergence rates for viscosity solutions
with bounded Hessians which may be piecewise smooth or degenerate.

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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th