List questions from sobolev-spaces

Published on 15 Apr 2026 - 20:54

705

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Density of smooth functions in $H^1(\Omega)$.

Published on 09 Apr 2026 - 10:45

425

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Bound L^2 norm of gradient by L^infinity norm

Published on 13 Apr 2026 - 23:17

55

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Sobolev spaces and Laplace transforms

Published on 25 Apr 2026 - 0:10

190

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Is there trace operator for periodic functions?

Published on 11 May 2026 - 1:01

43

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Is $H_0^1(\mathbb{R}) \cap H^2(\mathbb{R})$ compactly embedded into $L^2(\mathbb{R})$?

Published on 14 Apr 2026 - 18:08

52

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Why is this space Hilbert

Published on 16 Apr 2026 - 10:15

48

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difference quotient methods in L1

Published on 13 Apr 2026 - 17:56

34

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Is there a proof for this Theorem related to distributions and almost everywhere equality to 0?

Published on 13 Apr 2026 - 15:06

40

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Does it hold that $f_n \rightarrow f$ in $W^{1,2}(\Omega)$ imply $f_n \rightarrow f$ in $L^2(\Omega)$?

Published on 18 Apr 2026 - 15:47

47

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When is the function $f(x) = |x|^m$ in $W^{1,p}(B)$, where $B$ is the open unit ball in $\mathbb{R}^n$?

Published on 14 Apr 2026 - 5:01

195

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Suppose $U$ is connected and $u\in W^{1,p}(U)$ satisfies $Du = 0$ a.e. in $U$. Prove $u$ is constant a.e. in $U.$

Published on 14 Apr 2026 - 17:26

42

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$H^{-3/2}$ control of the laplacian of a function by means of $H^{1/2}$ norm in $\mathbb{R}^2$

Published on 14 Apr 2026 - 10:14

165

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Do we have $H^{-s}\cong H^s$?

Published on 10 Apr 2026 - 3:11

36

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Question in Sobolev space

Published on 12 Apr 2026 - 11:53

List Question

$\dot{H}^1\subset L^6 $

Density of smooth functions in $H^1(\Omega)$.

Bound L^2 norm of gradient by L^infinity norm

Sobolev spaces and Laplace transforms

Is there trace operator for periodic functions?

Is $H_0^1(\mathbb{R}) \cap H^2(\mathbb{R})$ compactly embedded into $L^2(\mathbb{R})$?

Why is this space Hilbert

difference quotient methods in L1

Is there a proof for this Theorem related to distributions and almost everywhere equality to 0?

Does it hold that $f_n \rightarrow f$ in $W^{1,2}(\Omega)$ imply $f_n \rightarrow f$ in $L^2(\Omega)$?

When is the function $f(x) = |x|^m$ in $W^{1,p}(B)$, where $B$ is the open unit ball in $\mathbb{R}^n$?

Suppose $U$ is connected and $u\in W^{1,p}(U)$ satisfies $Du = 0$ a.e. in $U$. Prove $u$ is constant a.e. in $U.$

$H^{-3/2}$ control of the laplacian of a function by means of $H^{1/2}$ norm in $\mathbb{R}^2$

Do we have $H^{-s}\cong H^s$?

Question in Sobolev space

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