Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundary regularity for $p$-harmonic functions and solutions of obstacle
  problems on unbounded sets in metric spaces   The theory of boundary regularity for $p$-harmonic functions is extended to
unbounded open sets in complete metric spaces with a doubling measure
supporting a $p$-Poincar\'e inequality, $1<p<\infty$. The barrier
classification of regular boundary points is established, and it is shown that
regularity is a local property of the boundary. We also obtain boundary
regularity results for solutions of the obstacle problem on open sets, and
characterize regularity further in several other ways.

4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol