List questions from sobolev-spaces

Published on 15 Apr 2026 - 21:20

115

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Why does $\int_{\Omega}\Delta u \frac{\partial u}{\partial t}dx=-\frac{1}{2}\frac{d }{d t}|u|^2_{H^1_0}$ hold?

Published on 16 Apr 2026 - 4:59

35

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In what the fact that there is a continuous operator $E:W^{1,p}(U)\to W^{1,p}(\mathbb R^n)$ is important?

Published on 16 Apr 2026 - 11:56

60

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Existence for elliptic equation with lower order term

Published on 12 Apr 2026 - 10:36

204

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Density of C∞ -divergence free functions

Published on 10 Apr 2026 - 17:30

84

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Explain why $\int_{\mathbb R^N}|\nabla u_r(x)|^p dx=r^p \int_{\mathbb{R}^N}|\nabla u(rx)|^p dx$

Published on 17 Apr 2026 - 13:49

255

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Continuous representative of functions in ${H_{0}}^1(\Omega)$

Published on 11 Apr 2026 - 10:17

228

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Positive solution of the PDE: $u_t=\Delta u+au-buv$, am I missing something?

Published on 28 Mar 2026 - 10:16

57

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(Scaling argument) Show there is $v=\lambda ^\alpha u(k^\beta x)$ s.t. $\|v\|_{L^q(D)}=\|v\|_{W^{1,p}(D)}=1$.

Published on 17 Apr 2026 - 10:26

96

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Inequality in $W^{1,\infty}(\Omega)$

Published on 10 Apr 2026 - 2:14

452

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A good book on Fractional Sobolev space.

Published on 26 Mar 2026 - 21:34

31

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Equivalence between two differential operators

Published on 11 Apr 2026 - 17:02

154

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Fractional Sobolev spaces

Published on 12 Apr 2026 - 17:59

967

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Periodic Sobolev Spaces

Published on 27 Mar 2026 - 22:03

156

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Motivation for the norm in $W^{s,p}(\Omega )$

Published on 26 Mar 2026 - 3:12

List Question

Fredholm index and spectral flow

Why does $\int_{\Omega}\Delta u \frac{\partial u}{\partial t}dx=-\frac{1}{2}\frac{d }{d t}|u|^2_{H^1_0}$ hold?

In what the fact that there is a continuous operator $E:W^{1,p}(U)\to W^{1,p}(\mathbb R^n)$ is important?

Existence for elliptic equation with lower order term

Density of C∞ -divergence free functions

Explain why $\int_{\mathbb R^N}|\nabla u_r(x)|^p dx=r^p \int_{\mathbb{R}^N}|\nabla u(rx)|^p dx$

Continuous representative of functions in ${H_{0}}^1(\Omega)$

Positive solution of the PDE: $u_t=\Delta u+au-buv$, am I missing something?

(Scaling argument) Show there is $v=\lambda ^\alpha u(k^\beta x)$ s.t. $\|v\|_{L^q(D)}=\|v\|_{W^{1,p}(D)}=1$.

Inequality in $W^{1,\infty}(\Omega)$

A good book on Fractional Sobolev space.

Equivalence between two differential operators

Fractional Sobolev spaces

Periodic Sobolev Spaces

Motivation for the norm in $W^{s,p}(\Omega )$

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