List questions from sobolev-spaces

Published on 27 Mar 2026 - 7:49

956

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Is the set of smooth functions with zero mean dense in the space of Sobolev functions with zero mean?

Published on 08 Feb 2015 - 23:30

124

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What does $|Du| \leq 1 $ a.e. mean for $u\in L^2(\mathbb{R}^n)$.

Published on 09 Feb 2015 - 20:11

1.8k

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Does the existence of weak derivatives require the lower order derivatives also to exist?

Published on 27 Mar 2026 - 10:46

78

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Is $W(0,T;H^1, L^2) \cap L^\infty(0,T;L^\infty(M))$ dense in $W(0,T;H^1, H^{-1})$?

Published on 26 Mar 2026 - 11:01

526

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Is $\|\nabla u\|_2$ a norm on $W^{1,2}(\mathbb{R}^N)$

Published on 12 Feb 2015 - 3:12

100

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The range of Sobolev spaces to which the function $r^\beta\sin\beta\theta$ belongs

Published on 13 Feb 2015 - 0:32

1.6k

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Fundamental theorem of calculus in Sobolev Space $H^1$

Published on 13 Feb 2015 - 1:07

655

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Lower semicontinuity of ${\dot{H}}^1$ norm

Published on 14 Feb 2015 - 14:30

42

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sequence in $H_0^1(0,1)\setminus D(0,1)$

Published on 16 Feb 2015 - 9:56

43

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Doubt about convergence of a sequence in $H^1(\mathbb{R}^3)$

Published on 17 Feb 2015 - 10:52

196

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How to integrate functions in n dimensional space?

Published on 17 Feb 2015 - 13:20

117

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how to use an embedding theorem to show existence of a solution

Published on 17 Feb 2015 - 20:02

72

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Extension of Sobolev function

Published on 18 Feb 2015 - 10:56

260

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question about density of Sobolev spaces

Published on 18 Feb 2015 - 23:11

List Question

Question about this problem If $u \in H^1(U)$, then $Du=0$ a.e. on the set $\{u=0\}$

Is the set of smooth functions with zero mean dense in the space of Sobolev functions with zero mean?

What does $|Du| \leq 1 $ a.e. mean for $u\in L^2(\mathbb{R}^n)$.

Does the existence of weak derivatives require the lower order derivatives also to exist?

Is $W(0,T;H^1, L^2) \cap L^\infty(0,T;L^\infty(M))$ dense in $W(0,T;H^1, H^{-1})$?

Is $\|\nabla u\|_2$ a norm on $W^{1,2}(\mathbb{R}^N)$

The range of Sobolev spaces to which the function $r^\beta\sin\beta\theta$ belongs

Fundamental theorem of calculus in Sobolev Space $H^1$

Lower semicontinuity of ${\dot{H}}^1$ norm

sequence in $H_0^1(0,1)\setminus D(0,1)$

Doubt about convergence of a sequence in $H^1(\mathbb{R}^3)$

How to integrate functions in n dimensional space?

how to use an embedding theorem to show existence of a solution

Extension of Sobolev function

question about density of Sobolev spaces

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