Affiliation:
1. Academy of Mathematics and Systems Science , Chinese Academy of Sciences , Beijing 100190 , P. R. China
Abstract
Abstract
Consider a mapping
f
:
X
→
Y
{f\colon X\to Y}
between two metric measure spaces.
We study generalized versions of the local Lipschitz number
Lip
f
{\operatorname{Lip}f}
,
as well as of the distortion number
H
f
{H_{f}}
that is used to define quasiconformal mappings.
Using these numbers, we give sufficient conditions for f being a BV mapping
f
∈
BV
loc
(
X
;
Y
)
{f\in\mathrm{BV}_{\mathrm{loc}}(X;Y)}
or a Newton–Sobolev mapping
f
∈
N
loc
1
,
p
(
X
;
Y
)
{f\in N_{\mathrm{loc}}^{1,p}(X;Y)}
, with
1
≤
p
<
∞
{1\leq p<\infty}
.
Subject
Applied Mathematics,Analysis