Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $L^p$ regularity theory for even order elliptic systems with
  antisymmetric first order potentials   Motivated by a challenging expectation of Rivi\`ere (2011), in the recent
interesting work of deLongueville-Gastel (2019), de Longueville and Gastel
proposed the following geometrical even order elliptic system \begin{equation*}
  \Delta^{m}u=\sum_{l=0}^{m-1}\Delta^{l}\left\langle V_{l},du\right\rangle
+\sum_{l=0}^{m-2}\Delta^{l}\delta\left(w_{l}du\right)\qquad \text{ in }
B^{2m}\label{eq: Longue-Gastel system} \end{equation*} which includes
polyharmonic mappings as special cases. Under minimal regularity assumptions on
the coefficient functions and an additional algebraic antisymmetry assumption
on the first order potential, they successfully established a conservation law
for this system, from which everywhere continuity of weak solutions follows.
This beautiful result amounts to a significant advance in the expectation of
Rivi\`ere.
  In this paper, we seek for the optimal interior regularity of the above
system, aiming at a more complete solution to the aforementioned expectation of
Rivi\`ere. Combining their conservation law and some new ideas together, we
obtain optimal H\"older continuity and sharp $L^p$ regularity theory, similar
to that of Sharp and Topping \cite{Sharp-Topping-2013-TAMS}, for weak solutions
to a related inhomogeneous system. Our results can be applied to study heat
flow and bubbling analysis for polyharmonic mappings.

23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom