Question

Finding non-trivial real numbers which satisfy all three of: $\sum_{i=1}^{n}a_i=0,\sum_{i=1}^{n}{a_i}^3=0$ and $\sum_{i=1}^{n}\lvert a_i\rvert=1.$

score 184 · Answer 1 · 2023-03-24 11:53:36

184

Views

Finding non-trivial real numbers which satisfy all three of: $\sum_{i=1}^{n}a_i=0,\sum_{i=1}^{n}{a_i}^3=0$ and $\sum_{i=1}^{n}\lvert a_i\rvert=1.$

Published on 24 Mar 2023 - 11:53

score 145 · Answer 2 · 2026-02-23 02:55:27

145

Views

On Poincaré Inequalities

Published on 23 Feb 2026 - 2:55

score 51 · Answer 3 · 2023-05-01 08:44:07

51

Views

How to prove this Sobolev inequality?

Published on 01 May 2023 - 8:44

score 63 · Answer 4 · 2023-05-04 06:10:29

63

Views

Limit of the function$f(x) = \frac{x-1}{x-x^a}$ in 1

Published on 04 May 2023 - 6:10

score 37 · Answer 5 · 2023-05-05 12:19:49

37

Views

proving $\left\lVert Z \right\rVert_{2} \leq \left\lVert Z \right\rVert_{1}^{\frac{1}{4}} \left\lVert Z \right\rVert_{3}^{\frac{3}{4}}$

Published on 05 May 2023 - 12:19

score 330 · Answer 6 · 2023-05-14 06:56:04

330

Views

Is $x^a $sin$(x^{-a})$ Hölder continuous?

Published on 14 May 2023 - 6:56

score 47 · Answer 7 · 2023-05-16 11:40:40

47

Views

Seeking source (and other solutions): If $a^{1/p}+c^{1/p}\leq b^{1/p}$ and $u^{1/(p+1)}+w^{1/(p+1)}\geq v^{1/(p+1)}$, then $ubc-vca+wab \ge 0$

Published on 16 May 2023 - 11:40

score 41 · Answer 8 · 2023-05-19 03:57:11

41

Views

bounding $(|\alpha|+1)^2+(x+|\alpha|)^2$

Published on 19 May 2023 - 3:57

score 751 · Answer 9 · 2026-03-25 23:42:37

751

Views

If $a,b,c\ge 0: ab+bc+ca=1$, find Min $P=\frac{1}{\sqrt{2a+bc}}+\frac{1}{\sqrt{2b+ca}}+\frac{1}{\sqrt{2c+ab}}$

Published on 25 Mar 2026 - 23:42

score 88 · Answer 10 · 2023-06-10 07:23:31

88

Views

If $u \in L^\infty(0, T; H) \cap L^2(0, T; V)$ then $(u \cdot \nabla)u \in L^{4/3}(0,T; L^{6/5})$

Published on 10 Jun 2023 - 7:23

score 181 · Answer 11 · 2023-06-11 02:00:31

181

Views

Is there a Holder inequality for vector-valued functions?

Published on 11 Jun 2023 - 2:00

score 44 · Answer 12 · 2023-06-11 18:06:44

44

Views

Help with Sobolev embeddings in the case of $m_{1}=m_{2}$

Published on 11 Jun 2023 - 18:06

score 182 · Answer 13 · 2023-06-13 11:40:32

182

Views

Prove: $\sqrt{\frac{a}{4a^2+bc}}+\sqrt{\frac{b}{4b^2+ac}}+\sqrt{\frac{c}{4c^2+ba}}\ge \frac{\sqrt{2}}{\sqrt{a+b+c}}.$

Published on 13 Jun 2023 - 11:40

score 52 · Answer 14 · 2023-06-15 20:51:43

52

Views

Showing that $f*g$ is continuous with $f\in L^p(\mathbb{R}^n), g\in L^q(\mathbb{R}^n)$

Published on 15 Jun 2023 - 20:51

score 120 · Answer 15 · 2023-07-05 07:20:48

120

Views

Show that $4(x^3 + y^3 + z^3 + 3) \geq 3(x+1)(y+1)(z+1)$ | Inequalities

Published on 05 Jul 2023 - 7:20

List Question

Finding non-trivial real numbers which satisfy all three of: $\sum_{i=1}^{n}a_i=0,\sum_{i=1}^{n}{a_i}^3=0$ and $\sum_{i=1}^{n}\lvert a_i\rvert=1.$

On Poincaré Inequalities

How to prove this Sobolev inequality?

Limit of the function$f(x) = \frac{x-1}{x-x^a}$ in 1

proving $\left\lVert Z \right\rVert_{2} \leq \left\lVert Z \right\rVert_{1}^{\frac{1}{4}} \left\lVert Z \right\rVert_{3}^{\frac{3}{4}}$

Is $x^a $sin$(x^{-a})$ Hölder continuous?

Seeking source (and other solutions): If $a^{1/p}+c^{1/p}\leq b^{1/p}$ and $u^{1/(p+1)}+w^{1/(p+1)}\geq v^{1/(p+1)}$, then $ubc-vca+wab \ge 0$

bounding $(|\alpha|+1)^2+(x+|\alpha|)^2$

If $a,b,c\ge 0: ab+bc+ca=1$, find Min $P=\frac{1}{\sqrt{2a+bc}}+\frac{1}{\sqrt{2b+ca}}+\frac{1}{\sqrt{2c+ab}}$

If $u \in L^\infty(0, T; H) \cap L^2(0, T; V)$ then $(u \cdot \nabla)u \in L^{4/3}(0,T; L^{6/5})$

Is there a Holder inequality for vector-valued functions?

Help with Sobolev embeddings in the case of $m_{1}=m_{2}$

Prove: $\sqrt{\frac{a}{4a^2+bc}}+\sqrt{\frac{b}{4b^2+ac}}+\sqrt{\frac{c}{4c^2+ba}}\ge \frac{\sqrt{2}}{\sqrt{a+b+c}}.$

Showing that $f*g$ is continuous with $f\in L^p(\mathbb{R}^n), g\in L^q(\mathbb{R}^n)$

Show that $4(x^3 + y^3 + z^3 + 3) \geq 3(x+1)(y+1)(z+1)$ | Inequalities

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