Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New projection and Korn estimates for a class of constant-rank operators
  on domains   We prove that if $\mathcal A: D(\mathcal A) \subset L^p(\Omega;V) \to
L^p(\Omega;W)$ is a $k$th order constant-rank differential operator with
maximal rank, then there exists a linear solution operator $\mathcal A^{-1}$
satisfying Sobolev regularity estimates. This allows us to construct a linear
projection $T : D(T) \subset L^p(\Omega;V) \to L^p(\Omega;V)$ satisfying the
estimate
  \[
  \|u - T u\|_{W^{k,p}(\Omega)} \le C \|\mathcal A u\|_{L^p(\Omega)}\,, \quad
\mathcal A(T u) = 0\,,
  \] for all sufficiently regular maps. The estimate generalizes Fuch's
distance estimate for the del-var operator, to operators such as the laplacian
and the divergence. On regular domains, the same estimates are (trivially)
observed for operators with finite dimensional null-space. When $\mathcal A$ is
only assumed to be of constant rank, we are able to show that the Sobolev
distance to the space of $\mathcal A$-harmonic maps is bounded by $\mathcal A
u$, that is,
  \[
  \min_{{v \in L^p(\Omega), \Delta_\mathcal A v = 0}} \|u -
v\|_{W^{k,p}(\Omega)} \le C \|\mathcal A u\|_{L^p(\Omega)}.
  \] Similar projection and distance estimates involving lower-order
derivatives are further discussed, as well as a plethora of examples and
applications with well-known operators.

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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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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: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph