List questions from sobolev-spaces

Published on 25 Mar 2026 - 21:31

93

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Lipschitz functions on $\mathbb R^n$ has bounded derivative

Published on 27 Mar 2026 - 13:20

87

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If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

Published on 26 Mar 2026 - 9:38

79

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Does $W^{1,2}$ convergence on compact subsets imply convergence on the entire domain?

Published on 22 Jun 2020 - 9:11

44

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Example for optimal gradient bounds in heat/poisson equation

Published on 22 Jun 2020 - 16:48

112

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Prove that $\int |\nabla u||\nabla v|+|u||v|\leq |u|_{H^1}|v|_{H^1}$

Published on 27 Mar 2026 - 2:37

435

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Sobolev Spaces inner product

Published on 25 Jun 2020 - 12:36

547

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Show that the function belongs to Sobolev space

Published on 25 Jun 2020 - 15:30

59

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Could this integral be estimated with a positive constant?

Published on 27 Jun 2020 - 15:41

113

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Riemannian manifold, Sobolev space

Published on 02 Jul 2020 - 9:49

93

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It is true that this integral converges to $0$?

Published on 02 Jul 2020 - 9:58

411

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Existence of sequence of $C^{\infty}$ functions to approximate a $W^{1, \infty}$ function

Published on 27 Mar 2026 - 11:46

47

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Density in Sobolev Space

Published on 03 Jul 2020 - 7:20

65

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Poincaré inequality in the space $H_{r}^{2}$

Published on 04 Jul 2020 - 12:30

496

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Sobolev space on a compact Riemannian manifold does not depend of the metric

Published on 04 Jul 2020 - 13:47

List Question

Is $H_0^1\ni u\mapsto(u\cdot\nabla)u$ Fréchet differentiable?

Lipschitz functions on $\mathbb R^n$ has bounded derivative

If $u\in H_0^1(\Lambda,\mathbb R^2)\cap H^2(\Lambda,\mathbb R^2)$, is $\nabla^\perp\cdot\Delta u\in L^2(\Lambda)$?

Does $W^{1,2}$ convergence on compact subsets imply convergence on the entire domain?

Example for optimal gradient bounds in heat/poisson equation

Prove that $\int |\nabla u||\nabla v|+|u||v|\leq |u|_{H^1}|v|_{H^1}$

Sobolev Spaces inner product

Show that the function belongs to Sobolev space

Could this integral be estimated with a positive constant?

Riemannian manifold, Sobolev space

It is true that this integral converges to $0$?

Existence of sequence of $C^{\infty}$ functions to approximate a $W^{1, \infty}$ function

Density in Sobolev Space

Poincaré inequality in the space $H_{r}^{2}$

Sobolev space on a compact Riemannian manifold does not depend of the metric

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