List questions from sobolev-spaces

Published on 30 May 2023 - 0:15

45

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Behavior of a function in $H^1_0(\mathbb{R})$ at the origin

Published on 30 May 2023 - 14:13

165

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If $f' \in L^2$, then $f$ also belongs in $L^2$?

Published on 05 Jun 2023 - 22:51

44

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Density of smooth functions on $(0,T)\times\Omega$ in $W(0,T)$

Published on 25 Mar 2026 - 11:14

68

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Counter example: Sobolev embedding

Published on 30 Mar 2026 - 4:43

73

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Dual space of Sobolev spaces induced by Elliptic equations

Published on 26 Mar 2026 - 16:06

35

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For what dimensions of $\Omega$ is the embedding $H^1(\Omega) \subset L^6(\Omega)$ continuous?

Published on 07 Jun 2023 - 12:56

32

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Decay rate of a functional norm.

Published on 27 Mar 2026 - 3:49

131

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Is $-(I-\Delta)$ an dissipative operator in the context of $L^p$ spaces?

Published on 30 Mar 2026 - 4:41

64

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Showing a bilinear form is coercive and continuous

Published on 27 Mar 2026 - 2:34

45

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Help with Sobolev embeddings in the case of $m_{1}=m_{2}$

Published on 26 Mar 2026 - 4:33

117

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Bounding $L^6$ norm by $L^2$

Published on 11 Jun 2023 - 22:08

49

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Composition of operators from $L_2$ to $H^1$

Published on 12 Jun 2023 - 8:35

44

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show inequality by using bramble hilbert lemma

Published on 12 Jun 2023 - 14:11

69

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If $f \in H^{1}(I)$, then $\|f\|_{H^{-1}} = \|f\|_{H^{1}}$ with $|I| < \infty$.

Published on 12 Jun 2023 - 15:32

List Question

The Sobolev inequality extends to powers of function.

Behavior of a function in $H^1_0(\mathbb{R})$ at the origin

If $f' \in L^2$, then $f$ also belongs in $L^2$?

Density of smooth functions on $(0,T)\times\Omega$ in $W(0,T)$

Counter example: Sobolev embedding

Dual space of Sobolev spaces induced by Elliptic equations

For what dimensions of $\Omega$ is the embedding $H^1(\Omega) \subset L^6(\Omega)$ continuous?

Decay rate of a functional norm.

Is $-(I-\Delta)$ an dissipative operator in the context of $L^p$ spaces?

Showing a bilinear form is coercive and continuous

Help with Sobolev embeddings in the case of $m_{1}=m_{2}$

Bounding $L^6$ norm by $L^2$

Composition of operators from $L_2$ to $H^1$

show inequality by using bramble hilbert lemma

If $f \in H^{1}(I)$, then $\|f\|_{H^{-1}} = \|f\|_{H^{1}}$ with $|I| < \infty$.

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