List questions from sobolev-spaces

Published on 15 Apr 2026 - 6:36

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Dual space of $H^1$

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Sobolev spaces doubt

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Sobolev space $H^s(\mathbb{R}^n)$ is an algebra with $2s>n$

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Holder estimates for the gradient of the solutions to the linear divergence form elliptic equation?

Published on 13 Apr 2026 - 22:44

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Density of Sobolev spaces

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Is this gradient an isomorphism on its range?

Published on 15 Apr 2026 - 10:23

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Is $W_0^{1,p}(\Omega)\cap L^\infty(\Omega)$ complete?

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Is the Sobolev embedding $W^{l,2}(\mathbb{R}^d) \rightarrow C_0(\mathbb{R}^d)$ compact?

Published on 15 Apr 2026 - 17:19

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$u\in W^{1,p}(\Omega)$ with $u\in L^q(\Omega)$. Does this implies that $v\in L^q(\Omega)$ for $v$ close to $u$?

Published on 16 Apr 2026 - 2:45

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Is $W_0^{1,p}(\Omega)\cap L^q(\Omega)$ Uniformly Convex?

Published on 15 Apr 2026 - 7:53

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$u\in W_0^{1,p}(\Omega)$. Is there $v\in W_0^{1,p}(\Omega)$ with $\int_\Omega uv=\infty$?

Published on 16 Apr 2026 - 13:15

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Short and elegant introduction to Sobolev spaces

Published on 12 Apr 2026 - 10:54

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How to establish the estimate?

Published on 10 Apr 2026 - 10:10

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Limit in norm of a Sobolev space

Published on 10 Apr 2026 - 21:53

List Question

The inclusion of Sobolev spaces

Dual space of $H^1$

Sobolev spaces doubt

Sobolev space $H^s(\mathbb{R}^n)$ is an algebra with $2s>n$

Holder estimates for the gradient of the solutions to the linear divergence form elliptic equation?

Density of Sobolev spaces

Is this gradient an isomorphism on its range?

Is $W_0^{1,p}(\Omega)\cap L^\infty(\Omega)$ complete?

Is the Sobolev embedding $W^{l,2}(\mathbb{R}^d) \rightarrow C_0(\mathbb{R}^d)$ compact?

$u\in W^{1,p}(\Omega)$ with $u\in L^q(\Omega)$. Does this implies that $v\in L^q(\Omega)$ for $v$ close to $u$?

Is $W_0^{1,p}(\Omega)\cap L^q(\Omega)$ Uniformly Convex?

$u\in W_0^{1,p}(\Omega)$. Is there $v\in W_0^{1,p}(\Omega)$ with $\int_\Omega uv=\infty$?

Short and elegant introduction to Sobolev spaces

How to establish the estimate?

Limit in norm of a Sobolev space

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