Question

Continuity of the derivative operator in $L^2$ (ANSWERED)

score 50 · Answer 1 · 2023-12-10 08:57:19

50

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Continuity of the derivative operator in $L^2$ (ANSWERED)

Published on 10 Dec 2023 - 8:57

score 30 · Answer 2 · 2026-03-25 22:03:04

30

Views

Functions in $H_0^s(U)$ disappear on their boundaries?

Published on 25 Mar 2026 - 22:03

score 58 · Answer 3 · 2026-03-27 02:37:29

58

Views

On partial integration of $W^{1,p}_0(U)$ functions and boundary terms.

Published on 27 Mar 2026 - 2:37

score 90 · Answer 4 · 2023-12-10 23:46:11

90

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Calderón-Zigmund duality for $\Delta u$ and $D^2 u$ in $L^p$-norm : reference request

Published on 10 Dec 2023 - 23:46

score 48 · Answer 5 · 2023-12-11 10:15:33

48

Views

Let $f$ have compact support and $-u''+u=f$ a.e. on $(0, 1)$. Is the support of $u$ a compact subset of $(0, 1)$?

Published on 11 Dec 2023 - 10:15

score 44 · Answer 6 · 2023-12-11 11:23:55

44

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Is there $(f_n)\subset C^\infty_c (I)$ such that $\|f_n - 1_{[a, b]} \|_{L^2 (I)} \to 0$ and $\| f_n'\|_{L^2 (I)} \to 0$?

Published on 11 Dec 2023 - 11:23

score 43 · Answer 7 · 2023-12-11 17:11:47

43

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Brezis' exercise 8.29.5: if $f \geq 0$ a.e. on $I$, then $T f \geq 0$ on $I$

Published on 11 Dec 2023 - 17:11

score 82 · Answer 8 · 2026-03-27 02:36:05

82

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$u, v \in H^1(\Omega)$, then the product $uv \in W^{1,3/2}(\Omega)$ for $\Omega \subset \mathbb{R}^3$?

Published on 27 Mar 2026 - 2:36

score 38 · Answer 9 · 2023-12-11 22:23:10

38

Views

Brezis' exercise 8.30.2: $a$ is a continuous and coercive bilinear form on $V$

Published on 11 Dec 2023 - 22:23

score 82 · Answer 10 · 2026-03-25 22:10:18

82

Views

Proving that a weighted Sobolev space is a Hilbert space

Published on 25 Mar 2026 - 22:10

score 80 · Answer 11 · 2026-04-01 04:59:18

80

Views

Does this second-order boundary-value problem have a unique solution when $k=1$?

Published on 01 Apr 2026 - 4:59

score 35 · Answer 12 · 2026-04-02 14:35:59

35

Views

Does $\Delta u\in H^{-1}(M)$ imply $u\in H^{1}(M)$?

Published on 02 Apr 2026 - 14:35

score 102 · Answer 13 · 2026-04-01 05:05:14

102

Views

Brezis' exercise 8.30.6: $u_n \to u$ in $H^2 (I)$

Published on 01 Apr 2026 - 5:05

score 71 · Answer 14 · 2026-04-01 05:05:20

71

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Brezis' exercise 8.30.7: what happens to the sequence $(u_n)$ if $k_n \to 1$?

Published on 01 Apr 2026 - 5:05

score 252 · Answer 15 · 2026-03-27 00:04:03

252

Views

Brezis' exercise 8.30.8: how to find the eigenvalues of this self-adjoint compact operator?

Published on 27 Mar 2026 - 0:04

List Question

Continuity of the derivative operator in $L^2$ (ANSWERED)

Functions in $H_0^s(U)$ disappear on their boundaries?

On partial integration of $W^{1,p}_0(U)$ functions and boundary terms.

Calderón-Zigmund duality for $\Delta u$ and $D^2 u$ in $L^p$-norm : reference request

Let $f$ have compact support and $-u''+u=f$ a.e. on $(0, 1)$. Is the support of $u$ a compact subset of $(0, 1)$?

Is there $(f_n)\subset C^\infty_c (I)$ such that $\|f_n - 1_{[a, b]} \|_{L^2 (I)} \to 0$ and $\| f_n'\|_{L^2 (I)} \to 0$?

Brezis' exercise 8.29.5: if $f \geq 0$ a.e. on $I$, then $T f \geq 0$ on $I$

$u, v \in H^1(\Omega)$, then the product $uv \in W^{1,3/2}(\Omega)$ for $\Omega \subset \mathbb{R}^3$?

Brezis' exercise 8.30.2: $a$ is a continuous and coercive bilinear form on $V$

Proving that a weighted Sobolev space is a Hilbert space

Does this second-order boundary-value problem have a unique solution when $k=1$?

Does $\Delta u\in H^{-1}(M)$ imply $u\in H^{1}(M)$?

Brezis' exercise 8.30.6: $u_n \to u$ in $H^2 (I)$

Brezis' exercise 8.30.7: what happens to the sequence $(u_n)$ if $k_n \to 1$?

Brezis' exercise 8.30.8: how to find the eigenvalues of this self-adjoint compact operator?

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