Affiliation:
1. Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa , Italy
2. Department of Mathematics , University of Hradec Králové , Rokitanského 62, 500 03 Hradec Králové ; and Faculty of Economics, University of South Bohemia, Studentská 13, Ceské Budejovice , Czech Republic
Abstract
Abstract
We show that, given a homeomorphism
f
:
G
→
Ω
{f:G\rightarrow\Omega}
where G is an open subset of
ℝ
2
{\mathbb{R}^{2}}
and Ω is an open subset of a 2-Ahlfors regular metric measure space supporting a weak
(
1
,
1
)
{(1,1)}
-Poincaré inequality, it holds
f
∈
BV
loc
(
G
,
Ω
)
{f\in{\operatorname{BV_{\mathrm{loc}}}}(G,\Omega)}
if and only if
f
-
1
∈
BV
loc
(
Ω
,
G
)
{f^{-1}\in{\operatorname{BV_{\mathrm{loc}}}}(\Omega,G)}
.
Further, if f satisfies the Luzin N and N
-
1
{{}^{-1}}
conditions, then
f
∈
W
loc
1
,
1
(
G
,
Ω
)
{f\in\operatorname{W_{\mathrm{loc}}^{1,1}}(G,\Omega)}
if and only if
f
-
1
∈
W
loc
1
,
1
(
Ω
,
G
)
{f^{-1}\in\operatorname{W_{\mathrm{loc}}^{1,1}}(\Omega,G)}
.
Subject
Applied Mathematics,Analysis
Reference32 articles.
1. L. Ambrosio,
Metric space valued functions of bounded variation,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (4) 17 (1990), no. 3, 439–478.
2. L. Ambrosio,
Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces,
Adv. Math. 159 (2001), no. 1, 51–67.
3. L. Ambrosio,
Fine properties of sets of finite perimeter in doubling metric measure spaces,
Set-Valued Var. Anal. 10 (2002), 111–128.
4. L. Ambrosio, V. Caselles, S. Masnou and J.-M. Morel,
Connected components of sets of finite perimeter and applications to image processing,
J. Eur. Math. Soc. (JEMS) 3 (2001), no. 1, 39–92.
5. L. Ambrosio, N. Gigli and G. Savaré,
Gradient Flows in Metric Spaces and in the Space of Probability Measures, 2nd ed.,
Lectures Math. ETH Zürich,
Birkhäuser, Basel, 2008.
Cited by
1 articles.
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