Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Dirichlet problem for p-harmonic functions with respect to the
  Mazurkiewicz boundary   In this paper we develop the Perron method for solving the Dirichlet problem
for the analog of the p-Laplacian, i.e. for p-harmonic functions, with
Mazurkiewicz boundary values. The setting considered here is that of metric
spaces, where the boundary of the domain in question is replaced with the
Mazurkiewicz boundary. Resolutivity for Sobolev and continuous functions, as
well as invariance results for perturbations on small sets, are obtained. We
use these results to improve the known resolutivity and invariance results for
functions on the standard (metric) boundary. We also illustrate the results of
this paper by discussing several examples.

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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg