List questions from weak-derivatives

Published on 13 Jun 2017 - 12:05

806

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Commutativity of weak partial derivatives. Don't follow proof.

Published on 25 Jun 2017 - 22:56

1.7k

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Help proving Leibniz rule for weak derivatives in Evans' PDEs.

Published on 27 Jun 2017 - 11:22

693

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evil derivative

Published on 27 Mar 2026 - 16:15

36

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Is true that $\sum_{|\alpha|=k}\sum_{|\beta|=m-k}\|D^{\alpha+\beta}u\|^p_{L_{p}(\Omega)}=|u|_{W^{m,p}(\Omega)}^p$?

Published on 05 Aug 2017 - 18:45

347

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Weak form for an equation with a first derivative?

Published on 09 Aug 2017 - 9:08

84

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Compactly supported weak solution : Help with proof

Published on 15 Aug 2017 - 18:08

597

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Existence of time derivative in Bochner space $L^2(0,T;H_0^1(U))$ (parabolic pde)

Published on 26 Mar 2026 - 16:07

565

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Product rule and integration by parts in Bochner Sobolev space $W^{1,1}(U)$

Published on 26 Mar 2026 - 16:06

406

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Does $F(x)=\int_0^xf(y)dy$ have a weak derivative?

Published on 23 Aug 2017 - 19:31

841

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Convergence in $L^p$ implies convergence of weak derivative

Published on 04 Sep 2017 - 17:22

227

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

Published on 30 Sep 2017 - 19:05

2k

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Can there exist a function that has a weak derivative, but is not differentiable almost everywhere?

Published on 13 Oct 2017 - 9:53

45

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Equality of generalized derivatives implies equality of classical derivatives

Published on 14 Oct 2017 - 19:50

133

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Question on application of the dominated convergence theorem in showing that $|f|$ is weakly differentiable

Published on 19 Oct 2017 - 19:29

List Question

Sobolev space on unit ball minus a line

Commutativity of weak partial derivatives. Don't follow proof.

Help proving Leibniz rule for weak derivatives in Evans' PDEs.

evil derivative

Is true that $\sum_{|\alpha|=k}\sum_{|\beta|=m-k}\|D^{\alpha+\beta}u\|^p_{L_{p}(\Omega)}=|u|_{W^{m,p}(\Omega)}^p$?

Weak form for an equation with a first derivative?

Compactly supported weak solution : Help with proof

Existence of time derivative in Bochner space $L^2(0,T;H_0^1(U))$ (parabolic pde)

Product rule and integration by parts in Bochner Sobolev space $W^{1,1}(U)$

Does $F(x)=\int_0^xf(y)dy$ have a weak derivative?

Convergence in $L^p$ implies convergence of weak derivative

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

Can there exist a function that has a weak derivative, but is not differentiable almost everywhere?

Equality of generalized derivatives implies equality of classical derivatives

Question on application of the dominated convergence theorem in showing that $|f|$ is weakly differentiable

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