Question

Does a diffeomorphism between manifolds induce an isomorphism of Sobolev spaces?

score 685 · Answer 1 · 2026-04-12 11:36:01

685

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Does a diffeomorphism between manifolds induce an isomorphism of Sobolev spaces?

Published on 12 Apr 2026 - 11:36

score 171 · Answer 2 · 2026-04-15 19:06:45

171

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proving "$C^1([−1,1])$ is dense in the given space with given norm"

Published on 15 Apr 2026 - 19:06

score 415 · Answer 3 · 2026-04-12 12:20:22

415

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Understanding a corollary to a theorem concerning Sobolev spaces

Published on 12 Apr 2026 - 12:20

score 1.8k · Answer 4 · 2026-04-13 23:46:28

1.8k

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Dependence of the Sobolev embedding constants on the domain

Published on 13 Apr 2026 - 23:46

score 746 · Answer 5 · 2026-04-13 00:15:51

746

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Equivalents norms in Sobolev Spaces

Published on 13 Apr 2026 - 0:15

score 144 · Answer 6 · 2026-04-17 10:24:14

144

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Example that $u\in W^{1,2}$, but $u \notin W^{1,3}$

Published on 17 Apr 2026 - 10:24

score 639 · Answer 7 · 2026-04-11 20:00:09

639

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Understanding a theorem concerning Sobolev spaces

Published on 11 Apr 2026 - 20:00

score 1.1k · Answer 8 · 2026-04-12 08:44:36

1.1k

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Question about definition of Sobolev spaces

Published on 12 Apr 2026 - 8:44

score 1.1k · Answer 9 · 2026-04-12 02:54:00

1.1k

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Question about Sobolev embedding theorem

Published on 12 Apr 2026 - 2:54

score 120 · Answer 10 · 2026-04-14 18:55:33

120

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Sobolev spaces for functions mapping to $\mathbb R^n$

Published on 14 Apr 2026 - 18:55

score 3.7k · Answer 11 · 2026-04-12 17:17:20

3.7k

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How is the acting of $H^{-1}$ on $H^1_0$ defined?

Published on 12 Apr 2026 - 17:17

score 89 · Answer 12 · 2026-04-15 23:38:24

89

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Is the functional $F(u) = \int_{\Omega} \langle (A_1(x)\chi_{\{u>0\}}+A_2(x)\chi_{\{u\le0\}}) \nabla u, \nabla u \rangle$ convex?

Published on 15 Apr 2026 - 23:38

score 1.2k · Answer 13 · 2026-04-13 23:27:18

1.2k

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Follow-up on Sobolev embedding theorem

Published on 13 Apr 2026 - 23:27

score 207 · Answer 14 · 2026-04-14 12:16:05

207

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Is the functional $F:H^{1}_{0}(\Omega) \longrightarrow \mathbb{R}$ given below weak lower semicontinuous?

Published on 14 Apr 2026 - 12:16

score 252 · Answer 15 · 2026-04-15 20:36:46

252

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Lemma 3.3 in the book of the Fanghua Lin

Published on 15 Apr 2026 - 20:36

List Question

Does a diffeomorphism between manifolds induce an isomorphism of Sobolev spaces?

proving "$C^1([−1,1])$ is dense in the given space with given norm"

Understanding a corollary to a theorem concerning Sobolev spaces

Dependence of the Sobolev embedding constants on the domain

Equivalents norms in Sobolev Spaces

Example that $u\in W^{1,2}$, but $u \notin W^{1,3}$

Understanding a theorem concerning Sobolev spaces

Question about definition of Sobolev spaces

Question about Sobolev embedding theorem

Sobolev spaces for functions mapping to $\mathbb R^n$

How is the acting of $H^{-1}$ on $H^1_0$ defined?

Is the functional $F(u) = \int_{\Omega} \langle (A_1(x)\chi_{\{u>0\}}+A_2(x)\chi_{\{u\le0\}}) \nabla u, \nabla u \rangle$ convex?

Follow-up on Sobolev embedding theorem

Is the functional $F:H^{1}_{0}(\Omega) \longrightarrow \mathbb{R}$ given below weak lower semicontinuous?

Lemma 3.3 in the book of the Fanghua Lin

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