Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the dimension of a certain measure in the plane   We study the Hausdorff dimension of a measure related to a positive weak
solution of a certain partial differential equation in a simply connected
domain in the plane.
  Our work generalizes work of Lewis and coauthors when the measure is $p$
harmonic and also for $p=2$, the well known theorem of Makarov regarding the
Hausdorff dimension of harmonic measure relative to a point in a simply
connected domain.

33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
1
The categories of this paper are: cs