List questions from sobolev-spaces

Published on 16 Apr 2026 - 19:03

57

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Is true that $(\nabla u(t), \nabla v'(t))_{L^2}=(u(t), v(t))_{H_0^1}$?

Published on 13 Apr 2026 - 21:41

376

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Weak derivative of a multivariable function and Sobolev spaces

Published on 14 Apr 2026 - 22:12

262

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Inner product and norm in $H^1_{per}([0,L])$

Published on 11 Apr 2026 - 23:06

700

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Evans PDE: $Du =0$ a.e. implies that $u$ is a constant a.e.

Published on 13 Apr 2026 - 23:05

99

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Is the product of an $L^1$ and an $H_0^1$ functions in bounded Omega integrable?

Published on 14 Apr 2026 - 20:21

446

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Properties about the Laplace Operator

Published on 09 Apr 2026 - 5:31

813

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The Sobolev Space $H^{1/2}(\partial \Omega)$ as the Quotient Space $H^1(\Omega)/\ker(\text{tr})$

Published on 25 Mar 2026 - 11:16

71

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On the relation between $H^{1/2}(\partial Ω)$ and $\left(\ker(\text{tr})\right)^\bot$

Published on 25 Mar 2026 - 12:48

46

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Weak star convergence problem

Published on 12 Apr 2026 - 20:10

58

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prove the bound in Hilbert space

Published on 13 Apr 2026 - 18:19

178

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Sobolev Inequality for $u \in W_{0}^{1,p}(\mathbb{R}^{n})$.

Published on 15 Apr 2026 - 11:23

65

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Representation Formula in $W_0^{1,2}$

Published on 11 Apr 2026 - 20:39

54

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Reflexivity of $L^2(W^{1,2})$

Published on 16 Apr 2026 - 10:12

112

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Minimum of the functional $F[f]=\int_0^1 f'(x)^2dx-\log \left(f\left(\frac{1}{2}\right)\right)$

Published on 17 Apr 2026 - 19:46

List Question

Show that $u \in H^1(\omega)$ implies $|u(0)|\leq\sqrt{2}\|u\|_{H^1}$

Is true that $(\nabla u(t), \nabla v'(t))_{L^2}=(u(t), v(t))_{H_0^1}$?

Weak derivative of a multivariable function and Sobolev spaces

Inner product and norm in $H^1_{per}([0,L])$

Evans PDE: $Du =0$ a.e. implies that $u$ is a constant a.e.

Is the product of an $L^1$ and an $H_0^1$ functions in bounded Omega integrable?

Properties about the Laplace Operator

The Sobolev Space $H^{1/2}(\partial \Omega)$ as the Quotient Space $H^1(\Omega)/\ker(\text{tr})$

On the relation between $H^{1/2}(\partial Ω)$ and $\left(\ker(\text{tr})\right)^\bot$

Weak star convergence problem

prove the bound in Hilbert space

Sobolev Inequality for $u \in W_{0}^{1,p}(\mathbb{R}^{n})$.

Representation Formula in $W_0^{1,2}$

Reflexivity of $L^2(W^{1,2})$

Minimum of the functional $F[f]=\int_0^1 f'(x)^2dx-\log \left(f\left(\frac{1}{2}\right)\right)$

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