List questions from sobolev-spaces

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fourier transform for $H_s$ function

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Dirac's delta defined as a linear functional acting on a continuous test functions

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A sobolev function with zero differential is constant

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Compact Sobolev Embedding

Published on 09 Apr 2026 - 20:13

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How to express and prove a smoothness/decay rate relationship between tempered distributions and their Fourier transforms?

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Evan's PDE question Chapter 5 problem 9

Published on 12 Apr 2026 - 19:14

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Monotone sum of a monotone sequence with another sequence, can we get any convergence properties?

Published on 14 Apr 2026 - 8:27

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Show that $f \in H^{\frac{1}{2}}$, using that $\iint_{\mathbb{T}^1\times \mathbb{T}^1} \frac{|f(x)-f(y)|^2}{sin^2(\pi(x-y))} \,dx\,dy < \infty$

Published on 15 Apr 2026 - 23:03

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Question regarding convergence is Sobolev spaces

Published on 15 Apr 2026 - 9:47

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$u\in W^{1,1}((0,1))$, $f\in C^1(\mathbb R)$, but: $f\circ u\notin W^{1,1}((0,1))$

Published on 16 Apr 2026 - 17:36

178

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Integration by part in Sobolev spaces

Published on 14 Apr 2026 - 1:21

702

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Proof of one version of Poincaré's inequality

Published on 13 Apr 2026 - 1:07

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Convergence in Sobolev spaces 2

Published on 11 Apr 2026 - 20:58

123

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Converse to standard Sobolev Proposition

Published on 13 Apr 2026 - 16:20

List Question

Is $L^1(0,T;V') \subset H^{-1}(0,T;H)$ for $V \subset H \subset V'$?

fourier transform for $H_s$ function

Dirac's delta defined as a linear functional acting on a continuous test functions

A sobolev function with zero differential is constant

Compact Sobolev Embedding

How to express and prove a smoothness/decay rate relationship between tempered distributions and their Fourier transforms?

Evan's PDE question Chapter 5 problem 9

Monotone sum of a monotone sequence with another sequence, can we get any convergence properties?

Show that $f \in H^{\frac{1}{2}}$, using that $\iint_{\mathbb{T}^1\times \mathbb{T}^1} \frac{|f(x)-f(y)|^2}{sin^2(\pi(x-y))} \,dx\,dy < \infty$

Question regarding convergence is Sobolev spaces

$u\in W^{1,1}((0,1))$, $f\in C^1(\mathbb R)$, but: $f\circ u\notin W^{1,1}((0,1))$

Integration by part in Sobolev spaces

Proof of one version of Poincaré's inequality

Convergence in Sobolev spaces 2

Converse to standard Sobolev Proposition

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