List questions from sobolev-spaces

Published on 03 Jan 2024 - 21:47

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A basic question about $H^1(\Omega)$ Sobolev space

Published on 27 Mar 2026 - 2:39

91

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Brezis' exercise 8.31.2: if $\int_I f=0$ then $\|u\|_{L^2(I)} \leq \frac{1}{(1+\pi^2)} \|f\|_{L^2(I)}$

Published on 29 Mar 2026 - 3:36

60

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Brezis' exercise 8.32.2: given $f \in H$ and $\varepsilon>0$, there exists a unique $u \in V$ satisfying a condition

Published on 06 Jan 2024 - 8:38

29

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Second mixed weak derivatives of function not absolutely continuous

Published on 06 Jan 2024 - 15:59

28

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Question on the definition of fractional sobolev norm

Published on 25 Mar 2026 - 22:04

42

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For $g \in H^1(\mathbb{R}^n)$, is it always true that $\lVert \Delta g \rVert_{H^{-1}} = \lVert \nabla g \rVert_{L^2}$?

Published on 07 Jan 2024 - 19:16

89

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Problems with the proof of theorem 2 in section 5.3 in LC Evans PDE book (second edition)

Published on 09 Jan 2024 - 19:26

56

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Analyzing the Laplace Operator in $W_0^{2,2}(\Omega)$: Integral Identities, Inequalities, and Weak Solution

Published on 11 Jan 2024 - 16:45

47

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Showing that Sobolev Space $H^m$ is in $L^\infty$

Published on 13 Jan 2024 - 18:27

49

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Equivalent norm on sobolev spaces

Published on 17 Jan 2024 - 21:30

30

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Brezis Proposition 9.3 alternative proof

Published on 19 Jan 2024 - 14:50

41

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Does restricting variables of a Sobolev function produces a Sobolev function?

Published on 19 Jan 2024 - 20:49

93

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Confusion about Fourier transform and fractional Sobolev space definition

Published on 08 Apr 2026 - 3:05

41

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Showing this inequality in a Sobolev space

Published on 23 Jan 2024 - 16:00

List Question

Interchanging limits and integrals for Cauchy sequences in $L^p$

A basic question about $H^1(\Omega)$ Sobolev space

Brezis' exercise 8.31.2: if $\int_I f=0$ then $\|u\|_{L^2(I)} \leq \frac{1}{(1+\pi^2)} \|f\|_{L^2(I)}$

Brezis' exercise 8.32.2: given $f \in H$ and $\varepsilon>0$, there exists a unique $u \in V$ satisfying a condition

Second mixed weak derivatives of function not absolutely continuous

Question on the definition of fractional sobolev norm

For $g \in H^1(\mathbb{R}^n)$, is it always true that $\lVert \Delta g \rVert_{H^{-1}} = \lVert \nabla g \rVert_{L^2}$?

Problems with the proof of theorem 2 in section 5.3 in LC Evans PDE book (second edition)

Analyzing the Laplace Operator in $W_0^{2,2}(\Omega)$: Integral Identities, Inequalities, and Weak Solution

Showing that Sobolev Space $H^m$ is in $L^\infty$

Equivalent norm on sobolev spaces

Brezis Proposition 9.3 alternative proof

Does restricting variables of a Sobolev function produces a Sobolev function?

Confusion about Fourier transform and fractional Sobolev space definition

Showing this inequality in a Sobolev space

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