List questions from sobolev-spaces

Published on 26 Mar 2026 - 7:58

180

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What domains of $\mathbb{R}^n$ have the property that $H^1(\Omega)=H^1_0(\Omega)$?

Published on 29 Mar 2026 - 14:25

1.6k

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Morrey's inequality

Published on 23 Jul 2014 - 22:25

452

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About Sobolev-Poincare inequality on compact manifolds

Published on 23 Jul 2014 - 22:25

297

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Trace theorem for Sobolev functions: what is the significance of continuous extension to the boundary?

Published on 25 Jul 2014 - 15:41

209

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Bounding the integral of a function by the integral of its derivative

Published on 26 Jul 2014 - 20:16

575

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Is Dirac's delta function well-defined at Lebesgue points?

Published on 27 Jul 2014 - 14:15

3.2k

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Hardy's inequality

Published on 28 Jul 2014 - 19:43

1.9k

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Can we characterize homogeneous Sobolev spaces by means of Sobolev embedding?

Published on 28 Mar 2026 - 11:34

688

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Calculus in an abstract space

Published on 31 Jul 2014 - 23:06

260

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Is Sobolev space $H^{s}(\mathbb R),$ for $s>\frac{1}{2},$ closed under point wise multiplication?

Published on 04 Aug 2014 - 10:59

63

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Can we expect, $h\ast \mu \in L^{2}(\mathbb R, (1+|x|^{2})^{s})$ for $h\in \mathcal{S}(\mathbb R), \mu\in M(\mathbb R)$ and $s>1/2$?

Published on 05 Aug 2014 - 7:29

190

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Global bounded solution of $u_{tt}=\Delta u-mu+h$ in the Hilbert space $X=H_{0}^{1}\left(\Omega\right)\times L^{2}\left(\Omega\right)$

Published on 05 Aug 2014 - 12:48

1.6k

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Rellich's theorem for Sobolev space on the torus

Published on 26 Mar 2026 - 10:58

446

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About the image of the trace operator for Sobolev spaces.

Published on 06 Aug 2014 - 22:58

List Question

Gagliardo-Nirenberg-Sobolev inequality

What domains of $\mathbb{R}^n$ have the property that $H^1(\Omega)=H^1_0(\Omega)$?

Morrey's inequality

About Sobolev-Poincare inequality on compact manifolds

Trace theorem for Sobolev functions: what is the significance of continuous extension to the boundary?

Bounding the integral of a function by the integral of its derivative

Is Dirac's delta function well-defined at Lebesgue points?

Hardy's inequality

Can we characterize homogeneous Sobolev spaces by means of Sobolev embedding?

Calculus in an abstract space

Is Sobolev space $H^{s}(\mathbb R),$ for $s>\frac{1}{2},$ closed under point wise multiplication?

Can we expect, $h\ast \mu \in L^{2}(\mathbb R, (1+|x|^{2})^{s})$ for $h\in \mathcal{S}(\mathbb R), \mu\in M(\mathbb R)$ and $s>1/2$?

Global bounded solution of $u_{tt}=\Delta u-mu+h$ in the Hilbert space $X=H_{0}^{1}\left(\Omega\right)\times L^{2}\left(\Omega\right)$

Rellich's theorem for Sobolev space on the torus

About the image of the trace operator for Sobolev spaces.

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