Question

How does $\| \nabla u \|_{L^2}^2 \leq C \|\nabla u \|_{L^2}$ imply $\| u\|_{W^{1,2}}^2 \leq \| u\|_{W^{1,2}}$?

score 249 · Answer 1 · 2026-03-25 09:18:53

249

Views

How does $\| \nabla u \|_{L^2}^2 \leq C \|\nabla u \|_{L^2}$ imply $\| u\|_{W^{1,2}}^2 \leq \| u\|_{W^{1,2}}$?

Published on 25 Mar 2026 - 9:18

score 128 · Answer 2 · 2026-03-25 09:18:53

128

Views

How to Calculate the norm of a matrix transform from $(R^n,\|\cdot\|_{\infty})$ to $(R^n,\|\cdot\|_{1})$

Published on 25 Mar 2026 - 9:18

score 164 · Answer 3 · 2026-03-25 09:13:59

164

Views

Find function with inequality for derivative

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score 44 · Answer 4 · 2026-03-25 09:21:29

44

Views

Sufficient conditions for the derivative of a quotient to be positive

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score 50 · Answer 5 · 2026-03-25 04:58:48

50

Views

Can we infer convergence in total variation distance from a Poincaré inequality?

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score 138 · Answer 6 · 2026-03-25 09:19:39

138

Views

Show that $\chi^2(\nu κ,μ)\le c\chi^2(\nu,μ)$ for all probability measures $\nu$ implies $\text{Var}_μ[κf]\le c\text{Var}_μ[f]$ for all $f\in L^2(μ)$?

Published on 25 Mar 2026 - 9:19

score 153 · Answer 7 · 2026-03-25 09:19:39

153

Views

Growth of the gradient of $f(x+y) \leq f(x) f(y)$

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score 50 · Answer 8 · 2026-03-25 09:21:42

50

Views

Doubt obtaining the inequality (3) via (1)

Published on 25 Mar 2026 - 9:21

score 38 · Answer 9 · 2026-04-10 10:00:29

38

Views

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score 106 · Answer 10 · 2026-03-25 09:20:35

106

Views

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score 317 · Answer 11 · 2026-03-25 09:17:09

317

Views

Is there an extension of Donsker's invariance principle for not identically distributed random variables?

Published on 25 Mar 2026 - 9:17

score 408 · Answer 12 · 2026-03-25 09:17:56

408

Views

Can we show that the determinant of this matrix is non-zero?

Published on 25 Mar 2026 - 9:17

score 52 · Answer 13 · 2026-03-25 09:20:35

52

Views

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score 46 · Answer 14 · 2026-03-25 09:18:26

46

Views

Improving an upper bound of a function $f$ that satisfies an inequality involving $\exp(f)$.

Published on 25 Mar 2026 - 9:18

score 116 · Answer 15 · 2026-03-25 09:17:09

116

Views

For a $C^{\infty}$ function, is it true that $|f'(x)| \leq 1$ implies that $|f(x)| \leq x$?

Published on 25 Mar 2026 - 9:17

List Question

How does $\| \nabla u \|_{L^2}^2 \leq C \|\nabla u \|_{L^2}$ imply $\| u\|_{W^{1,2}}^2 \leq \| u\|_{W^{1,2}}$?

How to Calculate the norm of a matrix transform from $(R^n,\|\cdot\|_{\infty})$ to $(R^n,\|\cdot\|_{1})$

Find function with inequality for derivative

Sufficient conditions for the derivative of a quotient to be positive

Can we infer convergence in total variation distance from a Poincaré inequality?

Show that $\chi^2(\nu κ,μ)\le c\chi^2(\nu,μ)$ for all probability measures $\nu$ implies $\text{Var}_μ[κf]\le c\text{Var}_μ[f]$ for all $f\in L^2(μ)$?

Growth of the gradient of $f(x+y) \leq f(x) f(y)$

Doubt obtaining the inequality (3) via (1)

Inequalities in functions

Inequality: Tell me I'm algebraically wrong

Is there an extension of Donsker's invariance principle for not identically distributed random variables?

Can we show that the determinant of this matrix is non-zero?

Inverting Linear System of Inequalities

Improving an upper bound of a function $f$ that satisfies an inequality involving $\exp(f)$.

For a $C^{\infty}$ function, is it true that $|f'(x)| \leq 1$ implies that $|f(x)| \leq x$?

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