Question

$-\Delta u = f$ in $L^2(0,T;H^{-1}(\Omega))$ (as opposed to $H^{-1}(\Omega)$)

score 135 · Answer 1 · 2026-03-26 11:01:09

135

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$-\Delta u = f$ in $L^2(0,T;H^{-1}(\Omega))$ (as opposed to $H^{-1}(\Omega)$)

Published on 26 Mar 2026 - 11:01

score 185 · Answer 2 · 2015-01-26 21:49:03

185

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How to compute the $H^{-s}(\Omega)$-norm of a function?

Published on 26 Jan 2015 - 21:49

score 116 · Answer 3 · 2026-04-08 16:30:11

116

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Relationships among different definitions of Sobolev spaces

Published on 08 Apr 2026 - 16:30

score 62 · Answer 4 · 2015-01-29 20:33:30

62

Views

Is $H^1(0,\infty) \subset C^0([0,\infty))$?

Published on 29 Jan 2015 - 20:33

score 2.1k · Answer 5 · 2026-03-27 10:46:12

2.1k

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How to prove the chain rule with respect to weak derivatives?

Published on 27 Mar 2026 - 10:46

score 1.1k · Answer 6 · 2015-02-01 00:47:06

1.1k

Views

Approximation of Sobolev space functions by smooth functions

Published on 01 Feb 2015 - 0:47

score 34 · Answer 7 · 2015-02-01 03:09:12

If given $F(u_k)\to F(u)$ and $F'(u_k)\nabla u_k \to F'(u)\nabla u$ in $L^p$, why we have $F(u) \in W^{1,p}$ and $\nabla F(u)=F'(u)\nabla u?$

score 729 · Answer 8 · 2015-02-02 18:31:57

729

Views

Poincare inequality on a domain for functions with mean value zero

Published on 02 Feb 2015 - 18:31

score 428 · Answer 9 · 2026-03-30 20:52:56

428

Views

Question of $u\in L^p(U)$ does not have a trace on $\partial U$.

Published on 30 Mar 2026 - 20:52

score 66 · Answer 10 · 2026-04-02 17:05:20

66

Views

The minimizing problem over a sequence of shrinking balls

Published on 02 Apr 2026 - 17:05

score 576 · Answer 11 · 2015-02-04 08:59:45

576

Views

Compact embedding of anisotropic Sobolev space

Published on 04 Feb 2015 - 8:59

score 63 · Answer 12 · 2015-02-05 23:10:08

63

Views

Characterization of Sobolev space $H^m(\mathbb R^n)$ with $m\in\mathbb N_0$?

Published on 05 Feb 2015 - 23:10

score 50 · Answer 13 · 2015-02-07 09:29:50

50

Views

Why this function is in $C^\infty((0,\infty);H^1(\Omega))$?

Published on 07 Feb 2015 - 9:29

score 173 · Answer 14 · 2026-04-08 14:26:03

173

Views

weak* convergence in Sobolev space

Published on 08 Apr 2026 - 14:26

score 69 · Answer 15 · 2026-03-26 09:18:11

69

Views

$ \int_{\mathbb R^d}\int_{\mathbb R^d}b(x,y)\,f(x)\,f(y)dx\,dy \leq ||b_+||_{L^2(\mathbb R^d\times \mathbb R^d)}||f||_{L^2(\mathbb R^d)}^2 $

Published on 26 Mar 2026 - 9:18

List Question

$-\Delta u = f$ in $L^2(0,T;H^{-1}(\Omega))$ (as opposed to $H^{-1}(\Omega)$)

How to compute the $H^{-s}(\Omega)$-norm of a function?

Relationships among different definitions of Sobolev spaces

Is $H^1(0,\infty) \subset C^0([0,\infty))$?

How to prove the chain rule with respect to weak derivatives?

Approximation of Sobolev space functions by smooth functions

If given $F(u_k)\to F(u)$ and $F'(u_k)\nabla u_k \to F'(u)\nabla u$ in $L^p$, why we have $F(u) \in W^{1,p}$ and $\nabla F(u)=F'(u)\nabla u?$

Poincare inequality on a domain for functions with mean value zero

Question of $u\in L^p(U)$ does not have a trace on $\partial U$.

The minimizing problem over a sequence of shrinking balls

Compact embedding of anisotropic Sobolev space

Characterization of Sobolev space $H^m(\mathbb R^n)$ with $m\in\mathbb N_0$?

Why this function is in $C^\infty((0,\infty);H^1(\Omega))$?

weak* convergence in Sobolev space

$ \int_{\mathbb R^d}\int_{\mathbb R^d}b(x,y)\,f(x)\,f(y)dx\,dy \leq ||b_+||_{L^2(\mathbb R^d\times \mathbb R^d)}||f||_{L^2(\mathbb R^d)}^2 $

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