List questions from weak-derivatives

Published on 17 Apr 2026 - 22:53

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Sobolev spaces in one-dimensional vs multidimensional

Published on 12 Apr 2026 - 17:19

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If $u \in L^2(0,T;L^2)$ and $u' \in L^2(0,T;H^{-1})$, is $u \in C^0([0,T];V)$ for some space $V$?

Published on 15 Apr 2026 - 18:55

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Heaviside function has no weak derivative on $(-1, 1)$

Published on 10 Apr 2026 - 12:47

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negative Sobolev space contains $L^1$ for a compact domain

Published on 14 Apr 2026 - 8:30

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Inverse Laplace operator $\Delta^{-1}$ and Sobolev spaces

Published on 13 Apr 2026 - 6:27

153

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Want to show $\lim_{\epsilon \to 0}\frac{1}{\epsilon} \int_0^T \langle u_t(t), T_\epsilon(u(t)) \rangle = \int_\Omega |u(T)| - \int_\Omega |u(0)|$

Published on 10 May 2026 - 17:39

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If $u \in L^2(0,T;H^1)$ has a distributional derivative $u' \in L^2(0,T;H^{-1})$, does $(u^+)' \in L^2(0,T;H^{-1})$ make sense?

Published on 10 May 2026 - 18:45

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Weak Derivative Heaviside function

Published on 10 Apr 2026 - 22:26

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Find a weak derivative of this function

Published on 15 Apr 2026 - 1:18

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Evans's proof of the Leibniz's formula for the weak derivatives in Sobolev spaces

Published on 10 Apr 2026 - 17:47

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A weak derivative of a function of two variable which depends only on one variable

Published on 14 Apr 2026 - 4:25

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Is $H^{1}(R;H^1(R^n))=H^1(R^{n+1})$?

Published on 15 Apr 2026 - 16:35

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Weak derivative and integration by parts

Published on 14 Apr 2026 - 2:35

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Weak derivatives equals zero

Published on 11 Apr 2026 - 7:59

List Question

Does weakly differentiable and $L^{\infty}$ imply continuity

Sobolev spaces in one-dimensional vs multidimensional

If $u \in L^2(0,T;L^2)$ and $u' \in L^2(0,T;H^{-1})$, is $u \in C^0([0,T];V)$ for some space $V$?

Heaviside function has no weak derivative on $(-1, 1)$

negative Sobolev space contains $L^1$ for a compact domain

Inverse Laplace operator $\Delta^{-1}$ and Sobolev spaces

Want to show $\lim_{\epsilon \to 0}\frac{1}{\epsilon} \int_0^T \langle u_t(t), T_\epsilon(u(t)) \rangle = \int_\Omega |u(T)| - \int_\Omega |u(0)|$

If $u \in L^2(0,T;H^1)$ has a distributional derivative $u' \in L^2(0,T;H^{-1})$, does $(u^+)' \in L^2(0,T;H^{-1})$ make sense?

Weak Derivative Heaviside function

Find a weak derivative of this function

Evans's proof of the Leibniz's formula for the weak derivatives in Sobolev spaces

A weak derivative of a function of two variable which depends only on one variable

Is $H^{1}(R;H^1(R^n))=H^1(R^{n+1})$?

Weak derivative and integration by parts

Weak derivatives equals zero

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