Question

How to prove that there exists a constant C such that $\max |f|^{2} \le C \int \left ( |f'|^{2} + f^{2} \right ) dx$?

score 203 · Answer 1 · 2026-04-14 16:03:12

203

Views

How to prove that there exists a constant C such that $\max |f|^{2} \le C \int \left ( |f'|^{2} + f^{2} \right ) dx$?

Published on 14 Apr 2026 - 16:03

score 98 · Answer 2 · 2026-04-15 19:33:11

98

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Equivalent inequalities

Published on 15 Apr 2026 - 19:33

score 35 · Answer 3 · 2026-04-12 01:37:16

35

Views

Unsure of an inequality and a certain step in a proof that shows $\Vert f \ast K_\delta - f \Vert_p \to 0 \ \text{as} \ \delta \to 0$?

Published on 12 Apr 2026 - 1:37

score 221 · Answer 4 · 2026-04-17 13:41:42

221

Views

Prove $(\langle x^4\rangle-\langle x^2\rangle^2)(\langle x^2\rangle-\langle x\rangle^2)>(\langle x^3\rangle-\langle x^2\rangle\langle x\rangle)^2$

Published on 17 Apr 2026 - 13:41

score 189 · Answer 5 · 2026-04-16 16:19:08

189

Views

Proving $\left\| \int_a^b f(x) \,dx\right\| \leq \int_a^b \| f(x) \|\, dx,$ for $f = (f_1,f_2,\dots,f_n):[a,b] \to \mathbb{R}^n$

Published on 16 Apr 2026 - 16:19

score 4.2k · Answer 6 · 2026-04-12 12:26:59

4.2k

Views

Proof of Gronwall inequality

Published on 12 Apr 2026 - 12:26

score 325 · Answer 7 · 2026-04-15 21:41:25

325

Views

Normal distribution inequality related to the monotone likelihood ratio property

Published on 15 Apr 2026 - 21:41

score 566 · Answer 8 · 2026-04-12 10:42:47

566

Views

Question on a proof of Wirtinger's Inequality

Published on 12 Apr 2026 - 10:42

score 56 · Answer 9 · 2026-04-12 03:14:37

56

Views

An(other) integral inequality

Published on 12 Apr 2026 - 3:14

score 2.7k · Answer 10 · 2026-04-16 10:51:35

2.7k

Views

Find the maximum $p$ such that $2x^4y^2 + 9y^4z^2 + 12z^4x^2 - px^2y^2z^2$ is always nonnegative for all $x$, $y$, and $z$ real.

Published on 16 Apr 2026 - 10:51

score 2.7k · Answer 11 · 2026-03-25 21:54:08

2.7k

Views

Prove that $\sqrt{ \frac{2x^2 - 2x + 1}{2} } \geq \frac{1}{x + \frac{1}{x}}$ for $0 < x < 1.$

Published on 25 Mar 2026 - 21:54

score 105 · Answer 12 · 2026-04-17 03:44:01

105

Views

Prove that $a + b + c + a^2 + b^2 + c^2 \leq4$ given that $a,b,c\geq-1$ and $a^3 + b^3 + c^3=1$

Published on 17 Apr 2026 - 3:44

score 166 · Answer 13 · 2026-04-16 01:27:47

166

Views

Is it true that $(\int f)^2 \le \int f^2$, $e^{\int f} \le \int e^f$?

Published on 16 Apr 2026 - 1:27

score 247 · Answer 14 · 2026-04-12 12:30:28

247

Views

Inequality involving exponential integral

Published on 12 Apr 2026 - 12:30

score 34 · Answer 15 · 2026-04-11 04:54:17

34

Views

norm of the differences of two definite integrals

Published on 11 Apr 2026 - 4:54

List Question

How to prove that there exists a constant C such that $\max |f|^{2} \le C \int \left ( |f'|^{2} + f^{2} \right ) dx$?

Equivalent inequalities

Unsure of an inequality and a certain step in a proof that shows $\Vert f \ast K_\delta - f \Vert_p \to 0 \ \text{as} \ \delta \to 0$?

Prove $(\langle x^4\rangle-\langle x^2\rangle^2)(\langle x^2\rangle-\langle x\rangle^2)>(\langle x^3\rangle-\langle x^2\rangle\langle x\rangle)^2$

Proving $\left\| \int_a^b f(x) \,dx\right\| \leq \int_a^b \| f(x) \|\, dx,$ for $f = (f_1,f_2,\dots,f_n):[a,b] \to \mathbb{R}^n$

Proof of Gronwall inequality

Normal distribution inequality related to the monotone likelihood ratio property

Question on a proof of Wirtinger's Inequality

An(other) integral inequality

Find the maximum $p$ such that $2x^4y^2 + 9y^4z^2 + 12z^4x^2 - px^2y^2z^2$ is always nonnegative for all $x$, $y$, and $z$ real.

Prove that $\sqrt{ \frac{2x^2 - 2x + 1}{2} } \geq \frac{1}{x + \frac{1}{x}}$ for $0 < x < 1.$

Prove that $a + b + c + a^2 + b^2 + c^2 \leq4$ given that $a,b,c\geq-1$ and $a^3 + b^3 + c^3=1$

Is it true that $(\int f)^2 \le \int f^2$, $e^{\int f} \le \int e^f$?

Inequality involving exponential integral

norm of the differences of two definite integrals

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