Question

Are smooth bounded-variation functions in the Sobolev Space $W_{1,1}$?

score 430 · Answer 1 · 2019-03-23 20:23:25

430

Views

Are smooth bounded-variation functions in the Sobolev Space $W_{1,1}$?

Published on 23 Mar 2019 - 20:23

score 69 · Answer 2 · 2019-03-31 00:54:28

69

Views

A short way to determine the divergence of the integral: $\int\limits_0^1 \left| \frac{1}{x}\cos\left(\frac{1}{x}\right) \right| dx$

Published on 31 Mar 2019 - 0:54

score 249 · Answer 3 · 2019-04-02 14:23:47

249

Views

Is there a function whose total variation is unbounded but its restricted variation (mesh converging to zero) is bounded?

Published on 02 Apr 2019 - 14:23

score 78 · Answer 4 · 2026-03-25 14:35:50

78

Views

If $f$ is nondecreasing and $h$ is of bounded variation with $|h(t)-h(s)|≤C\sqrt{f(t)-f(s)}$, then $\int|X||{\rm d}h|≤C\sqrt{\int|X|^2\:{\rm d}f}$

Published on 25 Mar 2026 - 14:35

score 57 · Answer 5 · 2026-03-25 06:13:00

57

Views

If $|\mu(E)|\le c\sqrt{\nu(E)}$ for all $E$ belonging to a generator, then the total variation of $\mu$ is bounded by $c\sqrt{\nu}$

Published on 25 Mar 2026 - 6:13

score 62 · Answer 6 · 2019-04-12 11:12:20

62

Views

How to prove that a function is of bounded outside variation?

Published on 12 Apr 2019 - 11:12

score 96 · Answer 7 · 2019-04-16 00:18:19

96

Views

Boundedness of derivative of logarithm functions.

Published on 16 Apr 2019 - 0:18

score 4.2k · Answer 8 · 2026-02-23 02:52:16

4.2k

Views

Absolute continuity, implies bounded variation.

Published on 23 Feb 2026 - 2:52

score 89 · Answer 9 · 2019-04-30 12:25:06

89

Views

Help with approximation of the length of a curve in $\mathbb{R}^n$

Published on 30 Apr 2019 - 12:25

score 760 · Answer 10 · 2019-05-04 09:07:25

760

Views

Some Questions about Regulated Functions

Published on 04 May 2019 - 9:07

score 60 · Answer 11 · 2019-05-05 04:16:14

60

Views

Prove $F(x)=\cos(x^{-1})\cdot\mathbf1_{x>0}$ is not of Bounded Variation on $[0,1]$

Published on 05 May 2019 - 4:16

score 878 · Answer 12 · 2019-05-15 08:20:36

878

Views

Functions of Bounded Variation Have Left and Right Limits

Published on 15 May 2019 - 8:20

score 300 · Answer 13 · 2019-05-19 20:14:19

300

Views

Sequence of bounded variation functions that converge uniformly to a function with unbounded variation

Published on 19 May 2019 - 20:14

score 137 · Answer 14 · 2019-05-21 16:41:31

137

Views

Total Variation of Subintervals

Published on 21 May 2019 - 16:41

score 163 · Answer 15 · 2019-05-25 21:48:03

163

Views

Bounded variation as a limit of sequence of partitions

Published on 25 May 2019 - 21:48

List Question

Are smooth bounded-variation functions in the Sobolev Space $W_{1,1}$?

A short way to determine the divergence of the integral: $\int\limits_0^1 \left| \frac{1}{x}\cos\left(\frac{1}{x}\right) \right| dx$

Is there a function whose total variation is unbounded but its restricted variation (mesh converging to zero) is bounded?

If $f$ is nondecreasing and $h$ is of bounded variation with $|h(t)-h(s)|≤C\sqrt{f(t)-f(s)}$, then $\int|X||{\rm d}h|≤C\sqrt{\int|X|^2\:{\rm d}f}$

If $|\mu(E)|\le c\sqrt{\nu(E)}$ for all $E$ belonging to a generator, then the total variation of $\mu$ is bounded by $c\sqrt{\nu}$

How to prove that a function is of bounded outside variation?

Boundedness of derivative of logarithm functions.

Absolute continuity, implies bounded variation.

Help with approximation of the length of a curve in $\mathbb{R}^n$

Some Questions about Regulated Functions

Prove $F(x)=\cos(x^{-1})\cdot\mathbf1_{x>0}$ is not of Bounded Variation on $[0,1]$

Functions of Bounded Variation Have Left and Right Limits

Sequence of bounded variation functions that converge uniformly to a function with unbounded variation

Total Variation of Subintervals

Bounded variation as a limit of sequence of partitions

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