Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity of weak solutions to higher order elliptic systems in
  critical dimensions   In this paper, we develop an elementary and unified treatment, in the spirit
of Rivi\`ere and Struwe (Comm. Pure. Appl. Math. 2008), to explore regularity
of weak solutions of higher order geometric elliptic systems in critical
dimensions without using conservation law. As a result, we obtain an interior
H\"older continuity for solutions of the higher order elliptic system of de
Longueville and Gastel \cite{deLongueville-Gastel-2019} in critical dimensions
$$\Delta^{k}u=\sum_{i=0}^{k-1}\Delta^{i}\left\langle V_{i},du\right\rangle
+\sum_{i=0}^{k-2}\Delta^{i}\delta\left(w_{i}du\right) \quad \text{in }
B^{2k},$$ under critical regularity assumptions on the coefficient functions.
This verifies an expectation of Rivi\`ere, and provides an affirmative answer
to an open question of Struwe in dimension four when $k=2$. The H\"older
continuity is also an improvement of the continuity result of Lamm and
Rivi\`ere and de Longueville and Gastel.

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The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci