Question

Some questions in the compactness of Sobolev space and Holder space

score 55 · Answer 1 · 2026-04-12 16:32:03

55

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Some questions in the compactness of Sobolev space and Holder space

Published on 12 Apr 2026 - 16:32

score 390 · Answer 2 · 2026-04-12 07:52:02

390

Views

Elliptic regularity for Poisson equation

Published on 12 Apr 2026 - 7:52

score 127 · Answer 3 · 2026-04-16 11:37:31

127

Views

Showing $\lVert \Delta u \rVert_{L^2} + \lVert u \rVert_{L^2}$ is equivalent to $\|u\|_{H^2}$ norm for $H^2$ space

Published on 16 Apr 2026 - 11:37

score 93 · Answer 4 · 2026-04-13 17:01:55

93

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Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

Published on 13 Apr 2026 - 17:01

score 83 · Answer 5 · 2026-04-16 11:03:20

83

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Proving $||f||^2_{L^2(\mathbb R^2)}\le 10||f||_{L^1(\mathbb R^2)}||\nabla f||_{L^2(\mathbb R^2)}$ with $f\in C^1,L^1\cap L^2$ and $\nabla f\in L^2$.

Published on 16 Apr 2026 - 11:03

score 423 · Answer 6 · 2026-04-14 08:21:33

423

Views

Hölder continuity on Sobolev space $H^1(a,b)$

Published on 14 Apr 2026 - 8:21

score 83 · Answer 7 · 2026-04-11 02:04:18

83

Views

Proof of the embedding of time dependent Sobolev spaces

Published on 11 Apr 2026 - 2:04

score 160 · Answer 8 · 2026-04-14 12:18:42

160

Views

Weak convergence in $H^1(\mathbb{R}^N)$ implies weak convergente in $H^1(B)$

Published on 14 Apr 2026 - 12:18

score 107 · Answer 9 · 2026-04-16 11:35:39

107

Views

Elliptic regularity with right-hand side in $H^{-1/2}$

Published on 16 Apr 2026 - 11:35

score 59 · Answer 10 · 2026-04-10 19:03:09

59

Views

How to the estimate as application of Strichartz Estimates?

Published on 10 Apr 2026 - 19:03

score 69 · Answer 11 · 2026-04-14 16:52:15

69

Views

Apply Arzela-Ascoli theorem to unifomly bounded sequence in $H^1$

Published on 14 Apr 2026 - 16:52

score 227 · Answer 12 · 2026-04-11 15:43:44

227

Views

Brezis book, Functional analysis, Sobolev spaces and PDE, problem 8.30

Published on 11 Apr 2026 - 15:43

score 114 · Answer 13 · 2026-04-13 17:09:28

114

Views

Equivalent definitions of Poincare inequality

Published on 13 Apr 2026 - 17:09

score 32 · Answer 14 · 2026-04-11 18:09:26

32

Views

Asking about proposition related to Sobolev and Bergman spaces

Published on 11 Apr 2026 - 18:09

score 46 · Answer 15 · 2026-04-16 16:55:42

46

Views

Is the set $\{\phi+\phi':\phi\in C^1_c(\mathbb{R})\}$ dense in $L^2(\mathbb{R})$?

Published on 16 Apr 2026 - 16:55

List Question

Some questions in the compactness of Sobolev space and Holder space

Elliptic regularity for Poisson equation

Showing $\lVert \Delta u \rVert_{L^2} + \lVert u \rVert_{L^2}$ is equivalent to $\|u\|_{H^2}$ norm for $H^2$ space

Prove the uniqueness of $u\in H_0^1(\Omega)$ with $\Delta u=\vert u\vert^{q-1}u+f$ in $\Omega$ with $\Omega$ as a bounded domain with smooth boundary.

Proving $||f||^2_{L^2(\mathbb R^2)}\le 10||f||_{L^1(\mathbb R^2)}||\nabla f||_{L^2(\mathbb R^2)}$ with $f\in C^1,L^1\cap L^2$ and $\nabla f\in L^2$.

Hölder continuity on Sobolev space $H^1(a,b)$

Proof of the embedding of time dependent Sobolev spaces

Weak convergence in $H^1(\mathbb{R}^N)$ implies weak convergente in $H^1(B)$

Elliptic regularity with right-hand side in $H^{-1/2}$

How to the estimate as application of Strichartz Estimates?

Apply Arzela-Ascoli theorem to unifomly bounded sequence in $H^1$

Brezis book, Functional analysis, Sobolev spaces and PDE, problem 8.30

Equivalent definitions of Poincare inequality

Asking about proposition related to Sobolev and Bergman spaces

Is the set $\{\phi+\phi':\phi\in C^1_c(\mathbb{R})\}$ dense in $L^2(\mathbb{R})$?

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