Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mappings with Integrable Dilatation in Higher Dimensions   Let $F\in W^{1,n}_{\text{loc}}(\Omega; \Bbb R^n)$ be a mapping with
nonnegative Jacobian $J_F(x)=\det DF(x)\ge 0$ for a.e. $x$ in a domain
$\Omega\subset\Bbb R^n$. The {\it dilatation} of $F$ is defined (almost
everywhere in $\Omega$) by the formula $$K(x)=\frac{|DF(x)|^n}{J_F(x)}\cdot$$
Iwaniec and \v Sver\' ak \ncite{IS} have conjectured that if $p\ge n-1$ and
$K\in L^{p}_{\text{loc}}(\Omega)$ then $F$ must be continuous, discrete and
open. Moreover, they have confirmed this conjecture in the two-dimensional case
$n=2$. In this article, we verify it in the higher- dimensional case $n\ge 2$
whenever $p>n-1$.

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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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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: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th