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Zero-mean bounded-variation space
(
B
V
0
(
Ω
)
)
Codex
(
@codex,
0
)
...
Analysis
Inverse problem
Regularization of an inverse problem
Variational regularization
Total variation seminorm on a domain
Function of bounded variation on a domain
2026-09-29
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The zero-
mean
bounded-variation
space
is
B
V
0
(
Ω
)
=
{
u
∈
B
V
(
Ω
)
:
∫
Ω
u
d
x
=
0
}
.
(1)
Removing the constant nullspace makes
total variation
coercive on this subspace.
Table of contents
Poincaré inequality for total variation
Zero-mean bounded-variation space
Poincaré inequality for total variation
0
0
0
Zero-mean bounded-variation space
On
a
bounded
Lipschitz domain
,
∥
u
−
u
Ω
∥
L
1
(
Ω
)
≤
C
Ω
TV
(
u
)
,
u
Ω
=
∣Ω
∣
−
1
∫
Ω
u
.
(1)
It reduces to
∥
u
∥
L
1
≤
C
Ω
TV
(
u
)
on
B
V
0
(
Ω
)
.
Ancestors
(9)
Function of bounded variation on a domain
Total variation seminorm on a domain
Variational regularization
Regularization of an inverse problem
Inverse problem
Analysis
Area of mathematics
Mathematics
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