Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisation of upper gradients on the weighted Euclidean space and
  applications   In the context of Euclidean spaces equipped with an arbitrary Radon measure,
we prove the equivalence among several different notions of Sobolev space
present in the literature and we characterise the minimal weak upper gradient
of all Lipschitz functions.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex