List questions from sobolev-spaces

Published on 16 Apr 2026 - 15:45

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Would you help me to understand which result from Sobolev Spaces or PDE are being used here?

Published on 14 Apr 2026 - 12:40

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Fourier Transform of Weak Derivative

Published on 12 Apr 2026 - 5:42

287

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Why define Sobolev spaces $W^{1,p}_0$ as completion of $C^1_c$ and not of $C^1_0$?

Published on 16 Apr 2026 - 8:54

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Are smooth functions a Sobolev space?

Published on 11 Apr 2026 - 17:40

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Estimating the $L^{\infty}$-norm of a Laplacian of a function

Published on 11 Apr 2026 - 17:03

318

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Show that $|x|^{-1/2}$ is not weakly differentiable

Published on 15 Apr 2026 - 18:37

279

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reverse poincare inequality for polynomials with vanishing boundary

Published on 14 Apr 2026 - 11:21

183

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Is there a name for the Sobolev Space $H^k$?

Published on 08 Apr 2026 - 17:11

149

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Does small interpolation error imply regularity of function?

Published on 10 Apr 2026 - 15:45

80

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How to show two norms are equivalent on periodic Sobolev space

Published on 13 Apr 2026 - 15:40

63

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$F : H_0^1 (\Omega,\mathbb{R}) \rightarrow L^2 (\Omega, \mathbb{R}), \ u \mapsto u^\gamma$ locally Lipschitz-continuous?

Published on 16 Apr 2026 - 5:22

322

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Poincaré inequality with special boundary condition?

Published on 12 Apr 2026 - 19:10

45

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Gagliardo-Nirenberg inequality with special boundary condition

Published on 10 Apr 2026 - 17:05

102

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Gagliardo–Nirenberg interpolation for $p=N=1$

Published on 15 Apr 2026 - 8:40

List Question

Are Sobolev spaces $W^{k,p}$ closed subsets of $L^p$?

Would you help me to understand which result from Sobolev Spaces or PDE are being used here?

Fourier Transform of Weak Derivative

Why define Sobolev spaces $W^{1,p}_0$ as completion of $C^1_c$ and not of $C^1_0$?

Are smooth functions a Sobolev space?

Estimating the $L^{\infty}$-norm of a Laplacian of a function

Show that $|x|^{-1/2}$ is not weakly differentiable

reverse poincare inequality for polynomials with vanishing boundary

Is there a name for the Sobolev Space $H^k$?

Does small interpolation error imply regularity of function?

How to show two norms are equivalent on periodic Sobolev space

$F : H_0^1 (\Omega,\mathbb{R}) \rightarrow L^2 (\Omega, \mathbb{R}), \ u \mapsto u^\gamma$ locally Lipschitz-continuous?

Poincaré inequality with special boundary condition?

Gagliardo-Nirenberg inequality with special boundary condition

Gagliardo–Nirenberg interpolation for $p=N=1$

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