List questions from sobolev-spaces

Published on 28 Jul 2020 - 6:46

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$u\in C^{\beta}[0,a]$ then $\int_{0}^{x} u(t) dt \in C^{\beta+1}[0,a]$

Published on 25 Mar 2026 - 12:27

117

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If $u \in H^1(\Omega)$ with $\Delta u \in L^2(\Omega)^*$, is $u \in H^2(\Omega)$?

Published on 26 Mar 2026 - 11:01

69

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Inequality in a Sobolev space

Published on 29 Jul 2020 - 21:28

38

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how can we use Sobolev embedding to get the following inequality?

Published on 30 Jul 2020 - 16:55

86

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Why does $ \frac{1 + |u|^p}{1 + |u|} \in L^{N/2}_{loc}(\Omega) $?

Published on 30 Jul 2020 - 18:16

440

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Question on Evans PDE book (Sobolev spaces involving time).

Published on 25 Mar 2026 - 19:03

436

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Is Laplacian of product of functions (one is smooth) square integrable?

Published on 26 Mar 2026 - 11:18

89

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Testing heat equation with $\log(u)$?

Published on 06 Jul 2016 - 7:51

77

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On convergence of particular functions in Sobolev space

Published on 06 Jul 2016 - 12:12

1.7k

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Is a weakly differentiable function differentiable almost everywhere?

Published on 26 Mar 2026 - 12:51

28

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I'm confused of the test problem of Weak Derivatives

Published on 06 Jul 2016 - 17:00

57

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Prove that $\left.F\right|_{\left\{ϕ∈C_c^∞(Ω,ℝ^d):∇⋅ϕ=0\right\}}=0⇔∃p∈C_c^∞(Ω)$ with $F=∇p$, for all $F∈H_0^1(Ω,ℝ^d)'$

Published on 27 Mar 2026 - 22:53

630

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How to show that a Schwartz distribution is in a Lebesgue or Sobolev space?

Published on 30 Mar 2026 - 16:48

99

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Approximation estimates in Sobolev spaces

Published on 26 Mar 2026 - 22:13

List Question

Inequality in Sobolev spaces: does it hold?

$u\in C^{\beta}[0,a]$ then $\int_{0}^{x} u(t) dt \in C^{\beta+1}[0,a]$

If $u \in H^1(\Omega)$ with $\Delta u \in L^2(\Omega)^*$, is $u \in H^2(\Omega)$?

Inequality in a Sobolev space

how can we use Sobolev embedding to get the following inequality?

Why does $ \frac{1 + |u|^p}{1 + |u|} \in L^{N/2}_{loc}(\Omega) $?

Question on Evans PDE book (Sobolev spaces involving time).

Is Laplacian of product of functions (one is smooth) square integrable?

Testing heat equation with $\log(u)$?

On convergence of particular functions in Sobolev space

Is a weakly differentiable function differentiable almost everywhere?

I'm confused of the test problem of Weak Derivatives

Prove that $\left.F\right|_{\left\{ϕ∈C_c^∞(Ω,ℝ^d):∇⋅ϕ=0\right\}}=0⇔∃p∈C_c^∞(Ω)$ with $F=∇p$, for all $F∈H_0^1(Ω,ℝ^d)'$

How to show that a Schwartz distribution is in a Lebesgue or Sobolev space?

Approximation estimates in Sobolev spaces

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