List questions from sobolev-spaces

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Application of Poincaré inequality

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Reference recommendation for sobolev space on the unit sphere

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Reguarity in $\mathbb{R}^2$

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Are the zeros same in $L^2$ and $\mathcal{S}'$?

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Verifying that the Sobolev space is a Banach Space

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chain rule for weak derivatives

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Gigliardo-Nirenberg-Sobolev inequality for functions in $W^{k,p}$, without zero trace.

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Consequence from Banach Theorem on $H^1(\Omega)$

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If $u\in W^{1,p}(\Omega)$ has support compactly inside $\Omega$, then $u\in W^{1,p}_0(\Omega)$

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$W^{1,p}(\Omega)$ V.S. $W^{1,p}_0(\Omega)$

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The regularity of elliptic equation

Published on 27 Mar 2026 - 2:34

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Trouble understanding proof of Sobolev trace theorem

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Obtaining this estimate

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Poincare inequality on $H^1_0(\mathbb{R}^2_+)$?

Published on 06 Jan 2015 - 22:33

List Question

Existence and regularity of solutions to parabolic equation on domain with disjoint boundary

Application of Poincaré inequality

Reference recommendation for sobolev space on the unit sphere

Reguarity in $\mathbb{R}^2$

Are the zeros same in $L^2$ and $\mathcal{S}'$?

Verifying that the Sobolev space is a Banach Space

chain rule for weak derivatives

Gigliardo-Nirenberg-Sobolev inequality for functions in $W^{k,p}$, without zero trace.

Consequence from Banach Theorem on $H^1(\Omega)$

If $u\in W^{1,p}(\Omega)$ has support compactly inside $\Omega$, then $u\in W^{1,p}_0(\Omega)$

$W^{1,p}(\Omega)$ V.S. $W^{1,p}_0(\Omega)$

The regularity of elliptic equation

Trouble understanding proof of Sobolev trace theorem

Obtaining this estimate

Poincare inequality on $H^1_0(\mathbb{R}^2_+)$?

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