List questions from sobolev-spaces

Published on 27 Mar 2026 - 21:32

38

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$H^1(\Omega')$ is in general not a subspace of $H^1 (\Omega)$ for bounded domains $\Omega' \subset \Omega$

Published on 22 Nov 2018 - 12:24

115

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A definite integral inequality

Published on 25 Mar 2026 - 4:35

81

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How to prove that a linear differential operator generates a semigroup?

Published on 25 Mar 2026 - 6:08

1k

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Sobolev spaces for vector-valued functions

Published on 25 Mar 2026 - 11:17

312

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Riesz representation and inverse operator.

Published on 26 Nov 2018 - 17:52

31

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an upper bound of a $d$ dimensional vector under a length constraint.

Published on 26 Nov 2018 - 22:51

398

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Is there a bounded domain on which Poincaré's inequality does not hold?

Published on 27 Mar 2026 - 16:53

98

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completion of $C^\infty_0(D)$ w.r.t $\|\cdot\|_\nabla$

Published on 26 Mar 2026 - 14:43

78

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Theorem in Adams Sobolev spaces book requires $u\in L^p(\Omega) \cap L^r(\Omega)$ but we only have $u \in C^\infty$ so how can theorem be applied?

Published on 29 Nov 2018 - 9:16

517

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Composition with Lipschitz map is Lipschitz on Sobolev spaces

Published on 25 Mar 2026 - 1:34

64

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How to show that the embedding is compact.

Published on 29 Nov 2018 - 16:29

121

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Compactly supported functions are dense in local Sobolev spaces

Published on 30 Nov 2018 - 13:31

80

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Distributional second-order derivatives of $\frac{e^{-|x|}}{4\pi |x|}$ to show the solution of $u -\Delta u=f$ is in $H^2$

Published on 26 Mar 2026 - 2:57

311

Views

Why weak convergence and a.e. convergence imply the convergence of this integral?

Published on 28 Mar 2026 - 13:42

List Question

How to choose the Testfunction-Space?

$H^1(\Omega')$ is in general not a subspace of $H^1 (\Omega)$ for bounded domains $\Omega' \subset \Omega$

A definite integral inequality

How to prove that a linear differential operator generates a semigroup?

Sobolev spaces for vector-valued functions

Riesz representation and inverse operator.

an upper bound of a $d$ dimensional vector under a length constraint.

Is there a bounded domain on which Poincaré's inequality does not hold?

completion of $C^\infty_0(D)$ w.r.t $\|\cdot\|_\nabla$

Theorem in Adams Sobolev spaces book requires $u\in L^p(\Omega) \cap L^r(\Omega)$ but we only have $u \in C^\infty$ so how can theorem be applied?

Composition with Lipschitz map is Lipschitz on Sobolev spaces

How to show that the embedding is compact.

Compactly supported functions are dense in local Sobolev spaces

Distributional second-order derivatives of $\frac{e^{-|x|}}{4\pi |x|}$ to show the solution of $u -\Delta u=f$ is in $H^2$

Why weak convergence and a.e. convergence imply the convergence of this integral?

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