Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of $p$-energy and associated energy measures on the
  Sierpi\'{n}ski carpet   We establish the existence of a scaling limit $\mathcal{E}_p$ of discrete
$p$-energies on the graphs approximating the planar Sierpi\'{n}ski carpet for
$p > \dim_{\text{ARC}}(\textsf{SC})$, where $\dim_{\text{ARC}}(\textsf{SC})$ is
the Ahlfors regular conformal dimension of the Sierpi\'{n}ski carpet.
Furthermore, the function space $\mathcal{F}_{p}$ defined as the collection of
functions with finite $p$-energies is shown to be a reflexive and separable
Banach space that is dense in the set of continuous functions with respect to
the supremum norm. In particular, $(\mathcal{E}_2, \mathcal{F}_2)$ recovers the
canonical regular Dirichlet form constructed by Barlow and Bass or Kusuoka and
Zhou. We also provide $\mathcal{E}_{p}$-energy measures associated with the
constructed $p$-energy and investigate its basic properties like
self-similarity and chain rule.

24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph