List questions from sobolev-spaces

Published on 08 Apr 2026 - 21:31

54

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Show that there exists a constant $C > 0$ such that $\lVert u\rVert_{H^1_0 (U)} ≤ C$ for all weak solutions $u$.

Published on 15 Apr 2026 - 18:37

44

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product Laplacian identity

Published on 14 Apr 2026 - 4:31

63

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What is the analytical solution of the one dimensional Poisson equation?

Published on 13 Apr 2026 - 14:56

72

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Is $\mathbb{R}^n_+$ an $(\varepsilon, \delta)$-domain?

Published on 10 May 2026 - 16:24

129

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Inequality involving a curl in two dimension

Published on 12 Apr 2026 - 5:22

24

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Is $\mathbb{R}^{d_1}\times (0,\infty)^{d_2}$ a $(\varepsilon, \delta)$-locally uniform domain?

Published on 10 May 2026 - 16:25

64

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Question about a possible consequence of Sobolev inequality

Published on 14 Apr 2026 - 4:04

107

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An inequality regarding $L^2$ and $H^{-1}$ norms

Published on 13 Apr 2026 - 4:04

256

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Existence of smooth solutions to the heat equation with variable coefficients

Published on 08 Apr 2026 - 21:09

191

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Sobolev spaces are isomorphic to $L^2$?

Published on 15 Apr 2026 - 9:16

54

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Distribution which is not in $H^{-1}(\mathbb{\Omega})$

Published on 09 Apr 2026 - 10:47

88

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Reference for a version of the Rellich-Kondrachov theorem for $L^1$ space into $BV$ space

Published on 16 Apr 2026 - 14:51

209

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Lower bound on $L^2$-norm of derivative

Published on 14 Apr 2026 - 23:49

78

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Convergence of time derivative in time-dependent Sobolev space

Published on 14 Apr 2026 - 8:20

List Question

How to apply Lax-Milgram theorem on one dimensional Poisson equation?

Show that there exists a constant $C > 0$ such that $\lVert u\rVert_{H^1_0 (U)} ≤ C$ for all weak solutions $u$.

product Laplacian identity

What is the analytical solution of the one dimensional Poisson equation?

Is $\mathbb{R}^n_+$ an $(\varepsilon, \delta)$-domain?

Inequality involving a curl in two dimension

Is $\mathbb{R}^{d_1}\times (0,\infty)^{d_2}$ a $(\varepsilon, \delta)$-locally uniform domain?

Question about a possible consequence of Sobolev inequality

An inequality regarding $L^2$ and $H^{-1}$ norms

Existence of smooth solutions to the heat equation with variable coefficients

Sobolev spaces are isomorphic to $L^2$?

Distribution which is not in $H^{-1}(\mathbb{\Omega})$

Reference for a version of the Rellich-Kondrachov theorem for $L^1$ space into $BV$ space

Lower bound on $L^2$-norm of derivative

Convergence of time derivative in time-dependent Sobolev space

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