List questions from sobolev-spaces

Published on 10 Apr 2026 - 10:21

187

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If a function is in $H^1(\Omega_i)$ then is $H^1(\Omega)$ in the whole domain?

Published on 16 Apr 2026 - 13:58

57

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About Poincare inequality

Published on 09 Apr 2026 - 5:06

908

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The trace theorem for functions in $H^{1/2}(\Omega)$

Published on 11 May 2026 - 7:47

270

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A domain satisfying the weak cone condition but not the strong cone condition

Published on 13 Apr 2026 - 23:59

136

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Consequence of a Sobolev's embedding into $L^{\infty}$

Published on 13 Apr 2026 - 17:40

47

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How to show there is no continuous trace operator from $W^{k,2}(R^m)$ to $W^{k,2}(R^{m-1})$?

Published on 14 Apr 2026 - 20:50

33

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Convergence in L^p for function multiplied for another function

Published on 12 Apr 2026 - 2:05

216

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Sobolev function has continuous representative

Published on 09 Apr 2026 - 0:23

98

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Proving this set is compact in $L^2(\Omega)$

Published on 09 Apr 2026 - 21:42

207

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Construct a solution of Laplace/Poisson problem with a non constant gradient jump

Published on 12 Apr 2026 - 1:19

44

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How to prove $C_{c}^{\infty}(R^{n}_{+})$ is not dense in $H^{m,p}(R_{+}^{n})$ when $m\geq 1$?

Published on 15 Apr 2026 - 0:19

57

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Improve the estimate constant

Published on 13 Apr 2026 - 18:07

163

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Clarification on Proof from Folland's Analysis - Sobolev Embedding Theorem

Published on 12 Apr 2026 - 7:18

88

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$f\in W^{1,2}(\mathbb R)$ and $\|xf(x)\|_2<\infty$ implies $\lim_{x\to\infty}x|f(x)|^2=0$

Published on 16 Apr 2026 - 18:57

List Question

Constant solution for an elliptic equation

If a function is in $H^1(\Omega_i)$ then is $H^1(\Omega)$ in the whole domain?

About Poincare inequality

The trace theorem for functions in $H^{1/2}(\Omega)$

A domain satisfying the weak cone condition but not the strong cone condition

Consequence of a Sobolev's embedding into $L^{\infty}$

How to show there is no continuous trace operator from $W^{k,2}(R^m)$ to $W^{k,2}(R^{m-1})$?

Convergence in L^p for function multiplied for another function

Sobolev function has continuous representative

Proving this set is compact in $L^2(\Omega)$

Construct a solution of Laplace/Poisson problem with a non constant gradient jump

How to prove $C_{c}^{\infty}(R^{n}_{+})$ is not dense in $H^{m,p}(R_{+}^{n})$ when $m\geq 1$?

Improve the estimate constant

Clarification on Proof from Folland's Analysis - Sobolev Embedding Theorem

$f\in W^{1,2}(\mathbb R)$ and $\|xf(x)\|_2<\infty$ implies $\lim_{x\to\infty}x|f(x)|^2=0$

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