Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A varifold perspective on the $p$-elastic energy of planar sets   Under suitable regularity assumptions the $p$-elastic energy of a planar set
$E\subset\mathbb{R}^2$ is defined to be
  $\int_{\partial E} 1 + |k_{\partial E}|^p \,\, d\mathcal{H}^1,$ where
$k_{\partial E}$ is the curvature of the boundary $\partial E$. In this work we
use a varifold approach to investigate this energy, that can be well defined on
varifolds with curvature. First we show new tools for the study of
1-dimensional curvature varifolds, such as existence and uniform bounds on the
density of varifolds with finite elastic energy. Then we characterize a new
notion of $L^1$-relaxation of this energy by extending the definition of
regular sets by an intrinsic varifold perspective, also comparing this
relaxation with the classical ones. Finally we discuss an application to the
inpainting problem, examples and qualitative properties of sets with finite
relaxed energy.

16
The categories of this paper are: stat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an