List questions from sobolev-spaces

Published on 14 Apr 2026 - 22:47

115

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If $u \in H_0^1(\Omega) \cap L^p(\Omega)$ and $\Delta u \in L^p(\Omega)$ then $u \in W^{2, p}(\Omega)$

Published on 16 Apr 2026 - 9:58

223

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How to show bilinear form is coercive?

Published on 11 Apr 2026 - 13:07

240

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A Sobolev space on a perforated domain with extension by a solid vector field

Published on 16 Apr 2026 - 6:58

181

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Sobolev space on the half-line

Published on 13 Apr 2026 - 8:46

68

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Is the notion of injective a.e. in the image well-defined for Sobolev maps?

Published on 14 Apr 2026 - 9:33

91

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References for $|u(x)|\leq C\, \|u\|_{W_{0}^{k,2}(\Omega)}\,\delta^{t} (x)$

Published on 15 Apr 2026 - 0:14

72

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A sequence of curves $(x_n)$ for which $g(\dot{x}_n, \dot{x}_n)$ is uniformly bounded converges weakly in $H^1([0, 1], M)$

Published on 17 Apr 2026 - 7:28

47

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Product estimate in multi-variable (non-isotropic) Sobolev Spaces $H^{s,r}(R^2)$

Published on 13 Apr 2026 - 3:10

127

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Sobolev Norm: Making sense of integral over $\mathbb{R}^{n^k}$ for $k \ge 1$

Published on 14 Apr 2026 - 10:02

430

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Basic questions about the sobolev space $H^\infty(\mathbb{R})$

Published on 11 Apr 2026 - 8:44

389

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Weak convergence of product of sequences that are weakly convergent in $H^1$ and weak-* convergent in $L^\infty$

Published on 15 Apr 2026 - 15:28

154

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PDE Sobolev Space, prove the equation holds weakly

Published on 14 Apr 2026 - 12:53

63

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Sobolev spaces exponents on Riemannian manifold

Published on 16 Apr 2026 - 21:16

97

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How to construct an example of a function inside $H^{1/2}(S^1)\setminus \mathcal{A}(S^1)$?

Published on 15 Apr 2026 - 6:59

List Question

Prove Leibniz' rule in $H^1$.

If $u \in H_0^1(\Omega) \cap L^p(\Omega)$ and $\Delta u \in L^p(\Omega)$ then $u \in W^{2, p}(\Omega)$

How to show bilinear form is coercive?

A Sobolev space on a perforated domain with extension by a solid vector field

Sobolev space on the half-line

Is the notion of injective a.e. in the image well-defined for Sobolev maps?

References for $|u(x)|\leq C\, \|u\|_{W_{0}^{k,2}(\Omega)}\,\delta^{t} (x)$

A sequence of curves $(x_n)$ for which $g(\dot{x}_n, \dot{x}_n)$ is uniformly bounded converges weakly in $H^1([0, 1], M)$

Product estimate in multi-variable (non-isotropic) Sobolev Spaces $H^{s,r}(R^2)$

Sobolev Norm: Making sense of integral over $\mathbb{R}^{n^k}$ for $k \ge 1$

Basic questions about the sobolev space $H^\infty(\mathbb{R})$

Weak convergence of product of sequences that are weakly convergent in $H^1$ and weak-* convergent in $L^\infty$

PDE Sobolev Space, prove the equation holds weakly

Sobolev spaces exponents on Riemannian manifold

How to construct an example of a function inside $H^{1/2}(S^1)\setminus \mathcal{A}(S^1)$?

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