Question

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

score 433 · Answer 1 · 2026-04-11 08:41:44

433

Views

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

Published on 11 Apr 2026 - 8:41

score 72 · Answer 2 · 2026-04-16 01:11:27

72

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 16 Apr 2026 - 1:11

score 252 · Answer 3 · 2026-04-12 07:03:15

252

Views

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

Published on 12 Apr 2026 - 7:03

score 79 · Answer 4 · 2026-05-10 17:02:38

79

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 10 May 2026 - 17:02

score 58 · Answer 5 · 2026-05-10 13:51:15

58

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 10 May 2026 - 13:51

score 67 · Answer 6 · 2026-04-17 01:00:05

67

Views

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

Published on 17 Apr 2026 - 1:00

score 99 · Answer 7 · 2026-04-12 08:49:52

99

Views

Boundedness of derivative of logarithm functions.

Published on 12 Apr 2026 - 8:49

score 4.3k · Answer 8 · 2026-04-15 12:57:10

4.3k

Views

Absolute continuity, implies bounded variation.

Published on 15 Apr 2026 - 12:57

score 92 · Answer 9 · 2026-04-15 19:26:13

92

Views

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

Published on 15 Apr 2026 - 19:26

score 764 · Answer 10 · 2026-04-10 23:32:31

764

Views

Some Questions about Regulated Functions

Published on 10 Apr 2026 - 23:32

score 63 · Answer 11 · 2026-04-14 16:15:09

63

Views

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

Published on 14 Apr 2026 - 16:15

score 881 · Answer 12 · 2026-04-12 16:08:42

881

Views

Functions of Bounded Variation Have Left and Right Limits

Published on 12 Apr 2026 - 16:08

score 303 · Answer 13 · 2026-04-12 18:12:53

303

Views

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

Published on 12 Apr 2026 - 18:12

score 141 · Answer 14 · 2026-04-10 19:58:11

141

Views

Total Variation of Subintervals

Published on 10 Apr 2026 - 19:58

score 166 · Answer 15 · 2026-04-10 13:34:51

166

Views

Bounded variation as a limit of sequence of partitions

Published on 10 Apr 2026 - 13:34

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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