Question

Is it true that $\operatorname{meas}(\partial(\operatorname{supp}(f)))=0$?

score 106 · Answer 1 · 2020-07-16 21:41:52

106

Views

Is it true that $\operatorname{meas}(\partial(\operatorname{supp}(f)))=0$?

Published on 16 Jul 2020 - 21:41

score 695 · Answer 2 · 2020-07-17 21:45:24

695

Views

Prove that there exists $c>0$ such that $\operatorname{supp}(f)\cap K \subset \{x \in K:|f(x)| \geq c\}+\{x \in \mathbb{R}^{n}:|x|<\varepsilon\}.$

Published on 17 Jul 2020 - 21:45

score 31 · Answer 3 · 2020-07-22 04:07:41

31

Views

Can we smooth a function on arbitrary small set with bounded $C^1$ norm?

Published on 22 Jul 2020 - 4:07

score 115 · Answer 4 · 2020-07-22 07:40:57

115

Views

Is this function defined through mean value theorem smooth enough?

Published on 22 Jul 2020 - 7:40

score 180 · Answer 5 · 2020-07-24 01:38:49

180

Views

Hessian at a maximum point lying on the boundary

Published on 24 Jul 2020 - 1:38

score 231 · Answer 6 · 2020-07-25 16:44:50

231

Views

How to reason about the smoothness of a function?

Published on 25 Jul 2020 - 16:44

score 166 · Answer 7 · 2020-07-27 20:05:44

166

Views

Smoothness of an even function of a square root

Published on 27 Jul 2020 - 20:05

score 44 · Answer 8 · 2020-07-28 12:48:44

44

Views

Smooth approximation: Does the position of the "middle value" remain the same?

Published on 28 Jul 2020 - 12:48

score 182 · Answer 9 · 2026-03-26 07:38:33

182

Views

Smooth functions into infinite dimensional Hilbert spaces

Published on 26 Mar 2026 - 7:38

score 842 · Answer 10 · 2026-03-25 17:28:18

842

Views

Smooth function between compact manifold and connected manifold

Published on 25 Mar 2026 - 17:28

score 328 · Answer 11 · 2017-04-05 20:16:29

328

Views

$f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$

Published on 05 Apr 2017 - 20:16

score 188 · Answer 12 · 2026-02-23 06:17:39

188

Views

Discontinuous function in Smooth infinitesimal analysis

Published on 23 Feb 2026 - 6:17

score 20 · Answer 13 · 2023-01-30 23:46:18

20

Views

Arbitrary parametrized functions determined by n points

Published on 30 Jan 2023 - 23:46

score 65 · Answer 14 · 2026-02-23 06:40:49

65

Views

Let $f \in \mathcal C_0$ and $\varepsilon >0$. Is there an explicit construction of $g\in\mathcal C_c^\infty$ such that $\|f-g\|_\infty <\varepsilon$?

Published on 23 Feb 2026 - 6:40

score 361 · Answer 15 · 2023-02-10 17:19:19

361

Views

Application of Mollifier function.

Published on 10 Feb 2023 - 17:19

List Question

Is it true that $\operatorname{meas}(\partial(\operatorname{supp}(f)))=0$?

Prove that there exists $c>0$ such that $\operatorname{supp}(f)\cap K \subset \{x \in K:|f(x)| \geq c\}+\{x \in \mathbb{R}^{n}:|x|<\varepsilon\}.$

Can we smooth a function on arbitrary small set with bounded $C^1$ norm?

Is this function defined through mean value theorem smooth enough?

Hessian at a maximum point lying on the boundary

How to reason about the smoothness of a function?

Smoothness of an even function of a square root

Smooth approximation: Does the position of the "middle value" remain the same?

Smooth functions into infinite dimensional Hilbert spaces

Smooth function between compact manifold and connected manifold

$f: \mathbb{R^2} \to \mathbb{R}$ a $C^\infty$ function such that $f(x,0)=f(0,y)=0$ then exists $g$ such that $f(x,y)=xy\, g(x,y)$

Discontinuous function in Smooth infinitesimal analysis

Arbitrary parametrized functions determined by n points

Let $f \in \mathcal C_0$ and $\varepsilon >0$. Is there an explicit construction of $g\in\mathcal C_c^\infty$ such that $\|f-g\|_\infty <\varepsilon$?

Application of Mollifier function.

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