Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Epsilon-regularity for p-harmonic maps at a free boundary on a sphere   We prove an $\epsilon$-regularity theorem for vector-valued p-harmonic maps,
which are critical with respect to a partially free boundary condition, namely
that they map the boundary into a round sphere.
  This does not seem to follow from the reflection method that Scheven used for
harmonic maps with free boundary (i.e., the case $p=2$): the reflected equation
can be interpreted as a $p$-harmonic map equation into a manifold, but the
regularity theory for such equations is only known for round targets.
  Instead, we follow the spirit of the last-named author's recent work on free
boundary harmonic maps and choose a good frame directly at the free boundary.
This leads to growth estimates, which, in the critical regime $p=n$, imply
H\"older regularity of solutions. In the supercritical regime, $p < n$, we
combine the growth estimate with the geometric reflection argument: the
reflected equation is super-critical, but, under the assumption of growth
estimates, solutions are regular.
  In the case $p<n$, for stationary $p$-harmonic maps with free boundary, as a
consequence of a monotonicity formula we obtain partial regularity up to the
boundary away from a set of $(n-p)$-dimensional Hausdorff measure.

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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn