List questions from integral-inequality

Published on 28 Mar 2026 - 13:21

31

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Whether $||a||_{L^p} +||b||_{L^p}\le||\sqrt{a^2+b^2}||_{L^p}$

Published on 14 Apr 2026 - 7:14

65

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Show that $\int_{|x|<R}\frac{|f(x)|}{|x|}\mathrm dx=o(R),\quad R\to\infty.$

Published on 14 Apr 2026 - 21:25

94

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An integral inequality with sequence

Published on 08 Apr 2026 - 17:07

145

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Proving an inequality involving integrals

Published on 11 Apr 2026 - 14:31

46

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Calculate limit value of sequence by inequation with integrals

Published on 14 Apr 2026 - 5:25

266

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Show that $\left(\int_{0}^{1}\sqrt{f(x)^2+g(x)^2}\ dx\right)^2 \geq \left(\int_{0}^{1} f(x)\ dx\right)^2 + \left(\int_{0}^{1} g(x)\ dx\right)^2$

Published on 17 Apr 2026 - 1:32

161

Views

Show $\left( \int_1^e f(x) \; dx \right)^2 \leq \int_1^e x\,f(x)^2 \; dx$

Published on 17 Apr 2026 - 16:27

69

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Where is that half coming from?

Published on 28 Mar 2026 - 13:27

96

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How can show $\left(1+\frac{1}{a}\right)\left(1-\frac{1}{\sqrt{2}}\int_{0}^{1}\sqrt{1+u^a}\,du\right)<1-1/\sqrt{2}$

Published on 17 Apr 2026 - 1:48

1.8k

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Prove uniqueness theoremn via Gronwall inequality

Published on 28 Mar 2026 - 12:48

47

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How to Proceed in Solving this Equation

Published on 09 Apr 2026 - 2:38

349

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How did he use Gronwall Lemma??

Published on 11 Apr 2026 - 3:28

246

Views

Inequality for moments of sums

Published on 09 Apr 2026 - 10:24

121

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Wirtinger's inequality

Published on 15 Apr 2026 - 23:53

List Question

How to show that $\int_\Omega \sum\limits_{i,j=1}^n u_{x_i}v_{x_j} dx\le C\int_\Omega |Du||Dv| dx$?

Whether $||a||_{L^p} +||b||_{L^p}\le||\sqrt{a^2+b^2}||_{L^p}$

Show that $\int_{|x|<R}\frac{|f(x)|}{|x|}\mathrm dx=o(R),\quad R\to\infty.$

An integral inequality with sequence

Proving an inequality involving integrals

Calculate limit value of sequence by inequation with integrals

Show that $\left(\int_{0}^{1}\sqrt{f(x)^2+g(x)^2}\ dx\right)^2 \geq \left(\int_{0}^{1} f(x)\ dx\right)^2 + \left(\int_{0}^{1} g(x)\ dx\right)^2$

Show $\left( \int_1^e f(x) \; dx \right)^2 \leq \int_1^e x\,f(x)^2 \; dx$

Where is that half coming from?

How can show $\left(1+\frac{1}{a}\right)\left(1-\frac{1}{\sqrt{2}}\int_{0}^{1}\sqrt{1+u^a}\,du\right)<1-1/\sqrt{2}$

Prove uniqueness theoremn via Gronwall inequality

How to Proceed in Solving this Equation

How did he use Gronwall Lemma??

Inequality for moments of sums

Wirtinger's inequality

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