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 248 · Answer 1 · 2026-03-22 12:08:04

248

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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 22 Mar 2026 - 12:08

score 127 · Answer 2 · 2026-03-22 00:04:29

127

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

Published on 22 Mar 2026 - 0:04

score 163 · Answer 3 · 2026-03-22 14:59:43

163

Views

Find function with inequality for derivative

Published on 22 Mar 2026 - 14:59

score 43 · Answer 4 · 2026-03-22 04:43:29

43

Views

Sufficient conditions for the derivative of a quotient to be positive

Published on 22 Mar 2026 - 4:43

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

50

Views

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

Published on 25 Mar 2026 - 4:58

score 137 · Answer 6 · 2026-03-22 11:45:08

137

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 22 Mar 2026 - 11:45

score 152 · Answer 7 · 2026-03-21 21:09:52

152

Views

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

Published on 21 Mar 2026 - 21:09

score 49 · Answer 8 · 2026-03-22 09:40:54

49

Views

Doubt obtaining the inequality (3) via (1)

Published on 22 Mar 2026 - 9:40

score 36 · Answer 9 · 2026-03-22 01:22:19

36

Views

Inequalities in functions

Published on 22 Mar 2026 - 1:22

score 105 · Answer 10 · 2026-03-21 16:06:53

105

Views

Inequality: Tell me I'm algebraically wrong

Published on 21 Mar 2026 - 16:06

score 316 · Answer 11 · 2026-03-22 14:18:08

316

Views

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

Published on 22 Mar 2026 - 14:18

score 407 · Answer 12 · 2026-03-22 15:45:01

407

Views

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

Published on 22 Mar 2026 - 15:45

score 51 · Answer 13 · 2026-03-22 00:08:35

51

Views

Inverting Linear System of Inequalities

Published on 22 Mar 2026 - 0:08

score 45 · Answer 14 · 2026-03-21 18:36:24

45

Views

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

Published on 21 Mar 2026 - 18:36

score 115 · Answer 15 · 2026-03-22 07:51:31

115

Views

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

Published on 22 Mar 2026 - 7:51

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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