Question

$C_c^{\infty}(\Omega) $ dense in $L^2(\mathbb{\Omega})$

score 1.9k · Answer 1 · 2026-04-11 02:57:27

1.9k

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$C_c^{\infty}(\Omega) $ dense in $L^2(\mathbb{\Omega})$

Published on 11 Apr 2026 - 2:57

score 618 · Answer 2 · 2026-04-12 07:18:27

618

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Simple question about $H^2 \cap H^1_0 (\Omega)$

Published on 12 Apr 2026 - 7:18

score 53 · Answer 3 · 2026-04-16 01:51:01

53

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Do the limits coincide? ($L^2$ and $H^2$)

Published on 16 Apr 2026 - 1:51

score 1.6k · Answer 4 · 2026-04-15 03:50:43

1.6k

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Neumann boundary condition VS Dirichlet boundary condition : Why Neumann condition don't need to be specified in the space?

Published on 15 Apr 2026 - 3:50

score 190 · Answer 5 · 2026-04-16 12:33:15

190

Views

$H^{-1}$'s norm: Is this true?

Published on 16 Apr 2026 - 12:33

score 1.3k · Answer 6 · 2026-04-11 09:29:25

1.3k

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Extension of Poincaré inequality: $\|u\|_{L^2(\Omega)}\leq C\|\nabla u\|_{L^2(\Omega)}$ when $u$ vanishes in $\Gamma\subseteq\partial\Omega$.

Published on 11 Apr 2026 - 9:29

score 165 · Answer 7 · 2026-04-13 21:49:37

165

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Relation between Lipschitz function and $W^{1,\infty}$

Published on 13 Apr 2026 - 21:49

score 349 · Answer 8 · 2026-04-12 00:08:59

349

Views

Sobolev embeddings; continuous representatives

Published on 12 Apr 2026 - 0:08

score 27 · Answer 9 · 2026-04-14 20:49:42

27

Views

A question about extension of functions in a manifold

Published on 14 Apr 2026 - 20:49

score 221 · Answer 10 · 2026-04-16 17:34:05

221

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The inclusion relations among Sobolev spaces: $W^{1,p}$, $W^{1,p}_0$ and $W^{1,p}_c$

Published on 16 Apr 2026 - 17:34

score 49 · Answer 11 · 2026-04-17 01:50:57

49

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Why $\varphi_n f_n\rightharpoonup\varphi f$ and $\varphi_n g_n\rightharpoonup \varphi g$ in $L^p$?

Published on 17 Apr 2026 - 1:50

score 157 · Answer 12 · 2026-04-16 18:16:13

157

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$W^{1,p}_0 \cap C^\infty \subset C^\infty_0$?

Published on 16 Apr 2026 - 18:16

score 977 · Answer 13 · 2026-04-15 19:08:29

977

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Is there any version of Sobolev embedding with respect to $W^{k,p}_0$, or for unbounded domain $\Omega\subset \mathbb R^n$?

Published on 15 Apr 2026 - 19:08

score 291 · Answer 14 · 2026-04-12 15:15:12

291

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Why the extension of distribution T in $(D(\Omega))^{'}$ to dual of sobolev space $W^{k,p}(\Omega)$ not unique?

Published on 12 Apr 2026 - 15:15

score 250 · Answer 15 · 2026-04-14 01:01:43

250

Views

Necessary condition for embedding of a homogeneous Sobolev space into the space of distributions

Published on 14 Apr 2026 - 1:01

List Question

$C_c^{\infty}(\Omega) $ dense in $L^2(\mathbb{\Omega})$

Simple question about $H^2 \cap H^1_0 (\Omega)$

Do the limits coincide? ($L^2$ and $H^2$)

Neumann boundary condition VS Dirichlet boundary condition : Why Neumann condition don't need to be specified in the space?

$H^{-1}$'s norm: Is this true?

Extension of Poincaré inequality: $\|u\|_{L^2(\Omega)}\leq C\|\nabla u\|_{L^2(\Omega)}$ when $u$ vanishes in $\Gamma\subseteq\partial\Omega$.

Relation between Lipschitz function and $W^{1,\infty}$

Sobolev embeddings; continuous representatives

A question about extension of functions in a manifold

The inclusion relations among Sobolev spaces: $W^{1,p}$, $W^{1,p}_0$ and $W^{1,p}_c$

Why $\varphi_n f_n\rightharpoonup\varphi f$ and $\varphi_n g_n\rightharpoonup \varphi g$ in $L^p$?

$W^{1,p}_0 \cap C^\infty \subset C^\infty_0$?

Is there any version of Sobolev embedding with respect to $W^{k,p}_0$, or for unbounded domain $\Omega\subset \mathbb R^n$?

Why the extension of distribution T in $(D(\Omega))^{'}$ to dual of sobolev space $W^{k,p}(\Omega)$ not unique?

Necessary condition for embedding of a homogeneous Sobolev space into the space of distributions

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