Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative stratification and higher regularity for biharmonic maps   In this paper we prove quantitative regularity results for stationary and
minimizing extrinsic biharmonic maps. As an application, we determine sharp,
dimension independent $L^p$ bounds for $\nabla^k f$ that do not require a small
energy hypothesis. In particular, every minimizing biharmonic map is in
$W^{4,p}$ for all $1\le p<5/4$. Further, for minimizing biharmonic maps from
$\Omega \subset \mathbb{R}^5$, we determine a uniform bound on the number of
singular points in a compact set. Finally, using dimension reduction arguments,
we extend these results to minimizing and stationary biharmonic maps into
special targets.

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The categories of this paper are: astro-ph
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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: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph