List questions from weak-derivatives

Published on 21 May 2014 - 7:14

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Sobolev spaces in one-dimensional vs multidimensional

Published on 01 Jun 2014 - 20:33

59

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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 03 Jun 2014 - 17:35

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

Published on 08 Jun 2014 - 15:27

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

Published on 15 Jun 2014 - 23:18

2.9k

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

Published on 20 Jun 2014 - 0:06

150

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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 25 Mar 2026 - 17:44

136

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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 25 Mar 2026 - 19:07

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Weak Derivative Heaviside function

Published on 27 Jun 2014 - 11:36

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Find a weak derivative of this function

Published on 11 Jul 2014 - 17:31

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

Published on 13 Jul 2014 - 20:08

276

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

Published on 15 Jul 2014 - 18:24

40

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

Published on 18 Jul 2014 - 13:13

3k

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Weak derivative and integration by parts

Published on 04 Sep 2014 - 16:18

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Weak derivatives equals zero

Published on 05 Sep 2014 - 8:07

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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