List questions from sobolev-spaces

43

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$\{u_m\}$ is bounded in $W^{1, p}(U)$, but does not possess a (norm-)convergent sequence in $L^{p^∗}(U)$

Published on 25 Mar 2026 - 19:25

44

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Weak convergence improved by Morrey embedding

Published on 28 Mar 2026 - 10:03

298

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Is the function in the $L^2$-sobolev space $H^{\frac{1}{2}} \ [- \pi, \pi]$ of order 1?

Published on 27 Mar 2026 - 19:55

335

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Prove that $W_0^{1,p}$ is a Banach space

Published on 27 Mar 2026 - 19:53

134

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Weak Formulation's Well-Posedness with Poincare-Friedrichs Inequality

Published on 16 Nov 2018 - 14:42

931

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Why is the laplacian a closed operator in $W^{2,p}(\mathbb{R}^n)$?

Published on 25 Mar 2026 - 9:26

54

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The spaces $L^p$ with $0<p<1$

Published on 18 Nov 2018 - 14:56

59

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prove that the space $C^{\infty}(R_{+}^n)\cap W^{1,2}(R_{+}^n)$ is dense in $W^{1,2}(R_{+}^n)$

Published on 18 Nov 2018 - 15:04

58

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Weak convergence in $H^1(\mathbb R^3)$ implies convergence of integrals

Published on 27 Mar 2026 - 2:39

93

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a question about Differential quotient operator in sobolev spaces

Published on 19 Nov 2018 - 6:33

232

Views

Variational problem of Laplace equation

Published on 19 Nov 2018 - 13:00

1.3k

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What is the orthogonal complement of $H^1_0$ in $H^1$?

Published on 26 Mar 2026 - 19:11

275

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Continuous embedding of weighted Lebesgue space

Published on 21 Nov 2018 - 8:07

112

Views

Equivalent definition for capacity in Sobolev spaces.

Published on 27 Mar 2026 - 23:01

145

Views

How can a discontinuous function belong to $C_B^1(\Omega)$, the space of continuous functions $u$ with bounded derivatives?

Published on 26 Mar 2026 - 13:00

List Question

$\{u_m\}$ is bounded in $W^{1, p}(U)$, but does not possess a (norm-)convergent sequence in $L^{p^∗}(U)$

Weak convergence improved by Morrey embedding

Is the function in the $L^2$-sobolev space $H^{\frac{1}{2}} \ [- \pi, \pi]$ of order 1?

Prove that $W_0^{1,p}$ is a Banach space

Weak Formulation's Well-Posedness with Poincare-Friedrichs Inequality

Why is the laplacian a closed operator in $W^{2,p}(\mathbb{R}^n)$?

The spaces $L^p$ with $0<p<1$

prove that the space $C^{\infty}(R_{+}^n)\cap W^{1,2}(R_{+}^n)$ is dense in $W^{1,2}(R_{+}^n)$

Weak convergence in $H^1(\mathbb R^3)$ implies convergence of integrals

a question about Differential quotient operator in sobolev spaces

Variational problem of Laplace equation

What is the orthogonal complement of $H^1_0$ in $H^1$?

Continuous embedding of weighted Lebesgue space

Equivalent definition for capacity in Sobolev spaces.

How can a discontinuous function belong to $C_B^1(\Omega)$, the space of continuous functions $u$ with bounded derivatives?

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