Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: H-log spaces of continuous functions, potentials, and elliptic boundary
  value problems   In these notes we study a family of Banach spaces, denoted $\,
D^{0,\,\al}(\Ov)\,,$ $\,\al \in\,\R^+\,,$ and called H-log spaces. For
$\,0<\,\la\leq\,1\,,$ one has $ C^{0,\,\la}(\Ov)\subset D^{0,\,\al}(\Ov)
\subset\,C(\Ov)\,,$ with compact embedding. These spaces present the following
"intermediate" regularity behavior. Solutions $\,u\,$ of second order linear
elliptic boundary value problems, under "external forces" $\,f\in\,
D^{0,\,\al}(\Ov)\,$ for some $\,\al>\,1\,,$ satisfy $\,\na^2\,u\in\,
D^{0,\,\al-\,1}(\Ov)\,$. This result is optimal, since $\,\na^2\,u\in\,
D^{0,\,\beta}(\Ov)\,,$ for some $\,\beta >\,\al-1\,,$ is false in general. We
present a preliminary study on this subject.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: cs
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The categories of this paper are: nucl-th