List questions from sobolev-spaces

Published on 09 Apr 2026 - 15:45

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Behaviour of functions in weighted sobolev spaces

Published on 04 Apr 2026 - 12:36

361

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Do we necessarily have that $W^{2, p}(I) \subset C^1(\overline{I})$ with compact injection?

Published on 17 Feb 2016 - 17:46

297

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Inequalities involving Sobolev spaces.

Published on 17 Feb 2016 - 20:24

33

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Do we have that $f \in W^{1, 1}(0, 1)$?

Published on 18 Feb 2016 - 0:29

175

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Are spherical harmonics a basis for $H^1$?

Published on 01 Apr 2026 - 18:22

137

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Two questions about a function in $W^{1, p}(0, 1)$.

Published on 13 Apr 2026 - 1:08

374

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Properties of function $f(x) = (1 + x^2)^{-\alpha/2}(\log(2+x^2))^{-1},\text{ }x \in \mathbb{R}$ with $0 < \alpha < 1$.

Published on 19 Feb 2016 - 17:19

209

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Does it necessarily follow that $C^{n, \gamma}(\overline{X})$ is a Banach space?

Published on 21 Feb 2016 - 23:28

3.8k

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If $u \in H^s(\mathbb{R}^n)$ for $s > n/2$, then $u \in L^\infty(\mathbb{R}^n)$?

Published on 22 Feb 2016 - 2:27

294

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Exists $C$ where $\int_{\mathbb{R}^n} {{u^2}\over{|x|^2}}\,dx \le C \int_{\mathbb{R}^n} |Du|^2\,dx$, $u \in H^1(\mathbb{R}^n)$?

Published on 22 Feb 2016 - 21:43

122

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Is it true that $\|Du\|_{L^{2p}} \le C\|u\|_{L^\infty}^{1\over2} \|D^2u\|_{L^p}^{1\over 2}$?

Published on 22 Feb 2016 - 21:55

1.1k

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Proof that bilinear form in $H_0^1$ is coercive

Published on 28 Mar 2026 - 8:10

364

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Does continuity imply weak differentiability?

Published on 09 Apr 2026 - 0:13

126

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Poisson equation, $L^2$ bounds

Published on 26 Mar 2026 - 21:25

List Question

Proof of equivalence of $\lambda$ norms in Sobolev space $H_0^1(\Omega)$

Behaviour of functions in weighted sobolev spaces

Do we necessarily have that $W^{2, p}(I) \subset C^1(\overline{I})$ with compact injection?

Inequalities involving Sobolev spaces.

Do we have that $f \in W^{1, 1}(0, 1)$?

Are spherical harmonics a basis for $H^1$?

Two questions about a function in $W^{1, p}(0, 1)$.

Properties of function $f(x) = (1 + x^2)^{-\alpha/2}(\log(2+x^2))^{-1},\text{ }x \in \mathbb{R}$ with $0 < \alpha < 1$.

Does it necessarily follow that $C^{n, \gamma}(\overline{X})$ is a Banach space?

If $u \in H^s(\mathbb{R}^n)$ for $s > n/2$, then $u \in L^\infty(\mathbb{R}^n)$?

Exists $C$ where $\int_{\mathbb{R}^n} {{u^2}\over{|x|^2}}\,dx \le C \int_{\mathbb{R}^n} |Du|^2\,dx$, $u \in H^1(\mathbb{R}^n)$?

Is it true that $\|Du\|_{L^{2p}} \le C\|u\|_{L^\infty}^{1\over2} \|D^2u\|_{L^p}^{1\over 2}$?

Proof that bilinear form in $H_0^1$ is coercive

Does continuity imply weak differentiability?

Poisson equation, $L^2$ bounds

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