Question

Integral Modulus Inequality

score 149 · Answer 1 · 2021-04-02 07:02:33

149

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Integral Modulus Inequality

Published on 02 Apr 2021 - 7:02

score 155 · Answer 2 · 2021-04-04 13:20:52

155

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Integral inequality (possible line integral)

Published on 04 Apr 2021 - 13:20

score 375 · Answer 3 · 2021-04-10 09:58:09

375

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Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Published on 10 Apr 2021 - 9:58

score 114 · Answer 4 · 2021-04-10 11:42:30

114

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Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$

Published on 10 Apr 2021 - 11:42

score 35 · Answer 5 · 2021-04-27 10:36:18

35

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How to prove the inequality $\iint_{x^2+y^2 \leq 1} e^{x^2+y^2}dxdy \leq (\int_{\sqrt{\pi}/2}^{\sqrt{\pi}/2} e^{x^2}dx)^2$

Published on 27 Apr 2021 - 10:36

score 89 · Answer 6 · 2021-05-10 20:56:57

89

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Lower bound via Sobolev Inequality

Published on 10 May 2021 - 20:56

score 43 · Answer 7 · 2021-05-11 17:40:42

43

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Lower bound for integral $\int_0^\infty (1+2ax)^{-3/2}(1+2bx)^{-n/2} dx$ when $a+nb=1$

Published on 11 May 2021 - 17:40

score 64 · Answer 8 · 2021-05-17 08:07:24

64

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Inequality involving the definite integrals of cos(x) f(x) and sin(x) f(x)

Published on 17 May 2021 - 8:07

score 139 · Answer 9 · 2021-05-17 09:32:37

139

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Inequality involving the definite integrals of $\cos(x) f(x)$ and $\sin(x) f(x)$

Published on 17 May 2021 - 9:32

score 95 · Answer 10 · 2021-05-17 10:08:22

95

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Inequality for $\int_Ω (F(f_1(x))-F(f_2(x)))(f_1(x)-f_2(x))\,\mathrm dx$ for an increasing function $F$

Published on 17 May 2021 - 10:08

score 79 · Answer 11 · 2021-05-24 10:45:41

79

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Hardy’s inequality. Exercise 3.14 from Rudin’s RACA.

Published on 24 May 2021 - 10:45

score 50 · Answer 12 · 2021-05-26 04:58:35

50

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Does $f'>0$ and $f''\ge\alpha f^p$ on $[t_0/2,t_0]$ imply $f'(x)>\sqrt{\frac\alpha{p+1}}\sqrt{f^{p+1}(x)-f^{p+1}\left(\frac{t_0}2\right)}$?

Published on 26 May 2021 - 4:58

score 46 · Answer 13 · 2021-05-31 14:26:40

46

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Boundedness of the minimizing sequence for Korn's inequality

Published on 31 May 2021 - 14:26

score 176 · Answer 14 · 2021-05-31 14:54:20

176

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Gronwall inequality for integrable functions

Published on 31 May 2021 - 14:54

score 204 · Answer 15 · 2021-06-10 10:12:16

204

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Bounding an integral by splitting the interval of integration

Published on 10 Jun 2021 - 10:12

List Question

Integral Modulus Inequality

Integral inequality (possible line integral)

Prove: $\overline{\int_{a}^{b}} (g+f)(x) \ dx = \int\limits_a^b {{f(x)}dx}+ \overline{\int_{a}^{b}} g(x) \ dx$

Finding $\min \frac{\left[\int_{0}^{1}f(x)\mathrm dx\right]^2}{\int_{0}^{1}(f(x))^3\mathrm dx}$ given that $f(0)=0$ and $0\lt f'(x)\le 1$

How to prove the inequality $\iint_{x^2+y^2 \leq 1} e^{x^2+y^2}dxdy \leq (\int_{\sqrt{\pi}/2}^{\sqrt{\pi}/2} e^{x^2}dx)^2$

Lower bound via Sobolev Inequality

Lower bound for integral $\int_0^\infty (1+2ax)^{-3/2}(1+2bx)^{-n/2} dx$ when $a+nb=1$

Inequality involving the definite integrals of cos(x) f(x) and sin(x) f(x)

Inequality involving the definite integrals of $\cos(x) f(x)$ and $\sin(x) f(x)$

Inequality for $\int_Ω (F(f_1(x))-F(f_2(x)))(f_1(x)-f_2(x))\,\mathrm dx$ for an increasing function $F$

Hardy’s inequality. Exercise 3.14 from Rudin’s RACA.

Does $f'>0$ and $f''\ge\alpha f^p$ on $[t_0/2,t_0]$ imply $f'(x)>\sqrt{\frac\alpha{p+1}}\sqrt{f^{p+1}(x)-f^{p+1}\left(\frac{t_0}2\right)}$?

Boundedness of the minimizing sequence for Korn's inequality

Gronwall inequality for integrable functions

Bounding an integral by splitting the interval of integration

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