List questions from sobolev-spaces

Published on 15 Apr 2026 - 0:22

71

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Weak $L^2$ convergence of Sobolev functions still Sobolev

Published on 16 Apr 2026 - 7:44

105

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Coercivity of a bilinear form in one dimesnion

Published on 27 Mar 2026 - 14:02

752

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When does a function in a Sobolev space also have bounded $L^\infty$ norm?

Published on 13 Apr 2026 - 2:40

152

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The equality of Sobolev norm and Lebesgue norm, $\|v\|_{-2} = \|v\|_{L^2}$

Published on 13 Apr 2026 - 2:00

69

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Why the existence of such an operator implies that $\mathcal C^1_c(\mathbb R^d)$ is dense in $W^{1,p}(\Omega )$?

Published on 13 Apr 2026 - 18:43

67

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Elementary question on Sobolev spaces and continuity

Published on 15 Apr 2026 - 0:14

463

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Showing Coercive Condition in Lax-Milgram

Published on 11 Apr 2026 - 20:43

741

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Example 3 Sobolev spaces Evans PDE

Published on 16 Apr 2026 - 10:31

357

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Let $H^k(\mathbb{R}^n)$ be the Sobolev space $W^{k,2}(\mathbb{R}^n)$. Do we have $H^2(\mathbb{R}^n) \subset\ H^1(\mathbb{R}^n)$?

Published on 14 Apr 2026 - 16:33

26

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Fixed point $u(x) = F(u)(x)$ properties

Published on 26 Mar 2026 - 19:38

1k

Views

Adjoint of the boundary trace operator?

Published on 09 Apr 2026 - 1:45

1.2k

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A weakly but not strongly convergent sequence in $H_0^1$

Published on 17 Apr 2026 - 4:16

276

Views

Sobolev space inclusion

Published on 10 Apr 2026 - 21:49

121

Views

Sobolev spaces ring domain

Published on 10 Apr 2026 - 16:27

List Question

Example of a function in Sobolev-Slobodeskji space

Weak $L^2$ convergence of Sobolev functions still Sobolev

Coercivity of a bilinear form in one dimesnion

When does a function in a Sobolev space also have bounded $L^\infty$ norm?

The equality of Sobolev norm and Lebesgue norm, $\|v\|_{-2} = \|v\|_{L^2}$

Why the existence of such an operator implies that $\mathcal C^1_c(\mathbb R^d)$ is dense in $W^{1,p}(\Omega )$?

Elementary question on Sobolev spaces and continuity

Showing Coercive Condition in Lax-Milgram

Example 3 Sobolev spaces Evans PDE

Let $H^k(\mathbb{R}^n)$ be the Sobolev space $W^{k,2}(\mathbb{R}^n)$. Do we have $H^2(\mathbb{R}^n) \subset\ H^1(\mathbb{R}^n)$?

Fixed point $u(x) = F(u)(x)$ properties

Adjoint of the boundary trace operator?

A weakly but not strongly convergent sequence in $H_0^1$

Sobolev space inclusion

Sobolev spaces ring domain

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