List questions from sobolev-spaces

Published on 13 Oct 2023 - 23:55

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Double integral of modulus of difference reference

Published on 14 Oct 2023 - 8:40

40

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Norm on $H^1/2(\partial\Omega)$ by first isomorphism theorem.

Published on 25 Mar 2026 - 20:34

25

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Does $f_{n} \rightharpoonup f$ in $H^{1}$ imply weak convergence in $L^{p}$?

Published on 15 Oct 2023 - 18:26

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Brezis' exercise 8.9.2: deduce that $v(x)=\frac{u(x)}{x} \in W^{1, p}(I)$ with $v(0)=0$

Published on 15 Oct 2023 - 21:03

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Brezis' exercise 8.9.3: check that $u_n \in W^{2, p}(I)$ and $u_n \rightarrow u$ in $W^{2, p}(I)$

Published on 15 Oct 2023 - 22:19

135

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Gilbarg Trudinger Interpolation inequality in Sobolev spaces

Published on 25 Mar 2026 - 9:11

20

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Brezis' exercise 8.9.5: $u \in X_m$ implies $\frac{D^j u(x)}{x^{m-j-k}} \in X_k$

Published on 16 Oct 2023 - 20:33

30

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Brezis' exercise 8.9.6: prove that $\zeta_n u \in W^{m, p}(I)$ and $\zeta_n u \to u$ in $W^{m, p}(I)$

Published on 16 Oct 2023 - 22:11

99

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Dense subspace of radial functions of $H^1(\mathbb{R}^N)$

Published on 25 Mar 2026 - 23:38

29

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Brezis' exercise 8.9.4: prove that $\frac{u(x)}{x^m} \in L^p(I)$ and $\frac{u(x)}{x^{m-1}} \in X_1$

Published on 17 Oct 2023 - 8:55

43

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Equivalent norms on space of ultra-distribution

Published on 02 Apr 2026 - 7:58

43

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Brezis' exercise 8.9.8: prove that $v \in W^{1,1}(I)$

Published on 17 Oct 2023 - 20:42

34

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A question about a bounded functional on $W^{1,2}(\Omega)$

Published on 19 Oct 2023 - 5:13

79

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Embedding of $\mathcal{D}(\Omega)$ in $W^{k,p}_0(\Omega)$

Published on 26 Mar 2026 - 9:49

List Question

Brezis' exercise 8.8.4: how to prove $u_n \to u$ in $W^{1, 1} (I)$?

Double integral of modulus of difference reference

Norm on $H^1/2(\partial\Omega)$ by first isomorphism theorem.

Does $f_{n} \rightharpoonup f$ in $H^{1}$ imply weak convergence in $L^{p}$?

Brezis' exercise 8.9.2: deduce that $v(x)=\frac{u(x)}{x} \in W^{1, p}(I)$ with $v(0)=0$

Brezis' exercise 8.9.3: check that $u_n \in W^{2, p}(I)$ and $u_n \rightarrow u$ in $W^{2, p}(I)$

Gilbarg Trudinger Interpolation inequality in Sobolev spaces

Brezis' exercise 8.9.5: $u \in X_m$ implies $\frac{D^j u(x)}{x^{m-j-k}} \in X_k$

Brezis' exercise 8.9.6: prove that $\zeta_n u \in W^{m, p}(I)$ and $\zeta_n u \to u$ in $W^{m, p}(I)$

Dense subspace of radial functions of $H^1(\mathbb{R}^N)$

Brezis' exercise 8.9.4: prove that $\frac{u(x)}{x^m} \in L^p(I)$ and $\frac{u(x)}{x^{m-1}} \in X_1$

Equivalent norms on space of ultra-distribution

Brezis' exercise 8.9.8: prove that $v \in W^{1,1}(I)$

A question about a bounded functional on $W^{1,2}(\Omega)$

Embedding of $\mathcal{D}(\Omega)$ in $W^{k,p}_0(\Omega)$

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