List questions from sobolev-spaces

Published on 16 Apr 2026 - 14:01

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Fundamental lemma of calculus of variations, gradients

Published on 12 Apr 2026 - 1:04

53

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A basic question about $W^{1,1}(\Omega)$

Published on 10 Apr 2026 - 3:32

197

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Inequality for function in certain Sobolev space

Published on 10 Apr 2026 - 13:49

126

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Does there exist a weak solution in $W^{1,2}_0(\Omega)$ to the following equation: $-\Delta u+bu=f$?

Published on 13 Apr 2026 - 23:58

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Bounded subsequence in Sobolev Space

Published on 10 Apr 2026 - 23:20

310

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Let $\Omega$ be a bounded open subset of $\mathbb{R^3}$, and $f$ be in $L^2(\Omega)$ Does there exist a weak solution in $W^{1,2}_0(\Omega)$

Published on 14 Apr 2026 - 6:51

273

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Prove that $\int_{D}\nabla u\cdot\nabla vdx=\int_{D}uv\,dx=0$

Published on 15 Apr 2026 - 22:37

298

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The equation $\,\,\Delta u+\cos u=0\,\,$ possesses a weak solution in $\,W^{1,2}_0(D)$

Published on 19 Apr 2026 - 15:12

825

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Extending weak solution to global weak solution of parabolic PDE

Published on 13 Apr 2026 - 0:23

242

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Compactness of the solution operator

Published on 08 Apr 2026 - 18:49

106

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Is $L^\infty(0,T;V)$ a reflexive space? Question about weak convergence

Published on 14 Apr 2026 - 9:01

369

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Selfadjointness of Coulomb Hamiltonian in $d\geq3$ dimensions

Published on 14 Apr 2026 - 5:44

498

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Weak periodic solution of parabolic PDE

Published on 15 Apr 2026 - 8:57

68

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If $(f_n)$ is Cauchy in the $L^2$-norm, then is $(f'_n)$ Cauchy in the $L^2$-norm?

Published on 14 Apr 2026 - 20:58

List Question

If $f_j \rightharpoonup f$ weakly in $W^{1,p}$ then $f_j \to f$ strongly in $L^p$?

Fundamental lemma of calculus of variations, gradients

A basic question about $W^{1,1}(\Omega)$

Inequality for function in certain Sobolev space

Does there exist a weak solution in $W^{1,2}_0(\Omega)$ to the following equation: $-\Delta u+bu=f$?

Bounded subsequence in Sobolev Space

Let $\Omega$ be a bounded open subset of $\mathbb{R^3}$, and $f$ be in $L^2(\Omega)$ Does there exist a weak solution in $W^{1,2}_0(\Omega)$

Prove that $\int_{D}\nabla u\cdot\nabla vdx=\int_{D}uv\,dx=0$

The equation $\,\,\Delta u+\cos u=0\,\,$ possesses a weak solution in $\,W^{1,2}_0(D)$

Extending weak solution to global weak solution of parabolic PDE

Compactness of the solution operator

Is $L^\infty(0,T;V)$ a reflexive space? Question about weak convergence

Selfadjointness of Coulomb Hamiltonian in $d\geq3$ dimensions

Weak periodic solution of parabolic PDE

If $(f_n)$ is Cauchy in the $L^2$-norm, then is $(f'_n)$ Cauchy in the $L^2$-norm?

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