List questions from bounded-variation

Published on 10 Oct 2015 - 3:24

34

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Bounded variations on $U-\{0\}$ $\Longrightarrow$ bounded variations on $U$?

Published on 22 Oct 2015 - 21:05

138

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If $f,f',f''$ are bounded a.e., is $f'$ of bounded variation everywhere?

Published on 23 Oct 2015 - 19:05

2.4k

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If a function is not continuous then is it possible for bounded function in given range?

Published on 24 Oct 2015 - 13:03

903

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Show that $ f \in BV[0, \pi] $ and find $ V_0^\pi f $ where $ f(x) = \cos^2(x) - 1, \;x \in [0,\pi] $

Published on 26 Oct 2015 - 18:21

515

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Given the function $ f(x) = \sin^2(\pi x) $, show that $ f \in BV[0, 1] $

Published on 28 Oct 2015 - 3:08

128

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Weak chain rule the other way round.

Published on 28 Oct 2015 - 14:17

631

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Approximation of Sets of Finite Perimeter

Published on 02 Nov 2015 - 0:53

93

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The zero convergence of total variation

Published on 02 Nov 2015 - 16:05

113

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The upper bound of $L^2$ norm of the minimizer in an minimizing problem.

Published on 27 Feb 2026 - 2:28

614

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Unbounded function of bounded variation (in $\mathbb R^d$, $d>1$)

Published on 10 Nov 2015 - 14:28

44

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Measure of vanishing set for BV function

Published on 11 Nov 2015 - 2:43

676

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total variation and monotonicy

Published on 13 Nov 2015 - 11:48

84

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If given conditions are satisfied, then prove that $f$ is absolutely continuous on any interval $[a,b]$

Published on 15 Nov 2015 - 1:56

498

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Difference of increasing functions differentiable a.e.

Published on 16 Nov 2015 - 7:48

List Question

Integrable absolutely continuous $f$ with integrable $f'$ has limit $0$ at infinity

Bounded variations on $U-\{0\}$ $\Longrightarrow$ bounded variations on $U$?

If $f,f',f''$ are bounded a.e., is $f'$ of bounded variation everywhere?

If a function is not continuous then is it possible for bounded function in given range?

Show that $ f \in BV[0, \pi] $ and find $ V_0^\pi f $ where $ f(x) = \cos^2(x) - 1, \;x \in [0,\pi] $

Given the function $ f(x) = \sin^2(\pi x) $, show that $ f \in BV[0, 1] $

Weak chain rule the other way round.

Approximation of Sets of Finite Perimeter

The zero convergence of total variation

The upper bound of $L^2$ norm of the minimizer in an minimizing problem.

Unbounded function of bounded variation (in $\mathbb R^d$, $d>1$)

Measure of vanishing set for BV function

total variation and monotonicy

If given conditions are satisfied, then prove that $f$ is absolutely continuous on any interval $[a,b]$

Difference of increasing functions differentiable a.e.

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