Question

Positive part of $y$ with $y\in L^2(0,T; H_0^1(\Omega))$ and $y'\in L^2(0,T; H^{-1}(\Omega))$

score 146 · Answer 1 · 2014-08-07 06:10:29

146

Views

Positive part of $y$ with $y\in L^2(0,T; H_0^1(\Omega))$ and $y'\in L^2(0,T; H^{-1}(\Omega))$

Published on 07 Aug 2014 - 6:10

score 181 · Answer 2 · 2014-08-07 12:09:39

181

Views

Limit of the p-norm of a function on subdomains equals the p-norm of the function on the union domain

Published on 07 Aug 2014 - 12:09

score 919 · Answer 3 · 2014-08-07 21:29:20

919

Views

How do the existence and $L^p$ integrability of weak derivative affect the smoothness of Sobolev functions?

Published on 07 Aug 2014 - 21:29

score 74 · Answer 4 · 2014-08-11 08:27:31

74

Views

Uniform continuity of weighted Sobolev functions.

Published on 11 Aug 2014 - 8:27

score 84 · Answer 5 · 2014-08-14 08:01:58

84

Views

What does local space of a given Banach space says intuitively?

Published on 14 Aug 2014 - 8:01

score 1.9k · Answer 6 · 2026-03-26 10:58:36

1.9k

Views

Compactness of the identity operator

Published on 26 Mar 2026 - 10:58

score 183 · Answer 7 · 2014-08-15 11:49:43

183

Views

Alternative derivation of Poincaré inequality

Published on 15 Aug 2014 - 11:49

score 133 · Answer 8 · 2026-03-28 13:28:05

133

Views

Embedding of weighted Lebesgue space on Fourier side into $C^\infty$

Published on 28 Mar 2026 - 13:28

score 264 · Answer 9 · 2026-03-25 11:25:36

264

Views

Weakening Sobolev coefficient in an elliptic estimate.

Published on 25 Mar 2026 - 11:25

score 43 · Answer 10 · 2026-03-28 13:21:26

43

Views

Is it true that, $x\rho(x/t)\in H^{s}$ for $\rho\in \mathcal{D}(\mathbb R)$ and $s>3/2$?

Published on 28 Mar 2026 - 13:21

score 102 · Answer 11 · 2026-03-28 13:21:33

102

Views

Example of a function $u\in L^\infty(0,T,H^1)$ such that $u_t\notin L^\infty(0,T,H^1)$

Published on 28 Mar 2026 - 13:21

score 1.4k · Answer 12 · 2014-08-20 10:25:13

1.4k

Views

Characterisation of one-dimensional Sobolev space

Published on 20 Aug 2014 - 10:25

score 1.3k · Answer 13 · 2014-08-21 12:56:32

1.3k

Views

Is $C^\infty_0$ dense in $C^\infty$ w.r.t. $\|\cdot\|_{L^p}$ and $\|\cdot\|_{W^{1,p}}$?

Published on 21 Aug 2014 - 12:56

score 982 · Answer 14 · 2014-08-21 13:16:56

982

Views

Boundedness of Volterra operator with Sobolev norm

Published on 21 Aug 2014 - 13:16

score 432 · Answer 15 · 2026-03-28 13:27:20

432

Views

Is $C(\mathbb R) \subset H_{s}^{loc}$ (localized Sobolev space)?

Published on 28 Mar 2026 - 13:27

List Question

Positive part of $y$ with $y\in L^2(0,T; H_0^1(\Omega))$ and $y'\in L^2(0,T; H^{-1}(\Omega))$

Limit of the p-norm of a function on subdomains equals the p-norm of the function on the union domain

How do the existence and $L^p$ integrability of weak derivative affect the smoothness of Sobolev functions?

Uniform continuity of weighted Sobolev functions.

What does local space of a given Banach space says intuitively?

Compactness of the identity operator

Alternative derivation of Poincaré inequality

Embedding of weighted Lebesgue space on Fourier side into $C^\infty$

Weakening Sobolev coefficient in an elliptic estimate.

Is it true that, $x\rho(x/t)\in H^{s}$ for $\rho\in \mathcal{D}(\mathbb R)$ and $s>3/2$?

Example of a function $u\in L^\infty(0,T,H^1)$ such that $u_t\notin L^\infty(0,T,H^1)$

Characterisation of one-dimensional Sobolev space

Is $C^\infty_0$ dense in $C^\infty$ w.r.t. $\|\cdot\|_{L^p}$ and $\|\cdot\|_{W^{1,p}}$?

Boundedness of Volterra operator with Sobolev norm

Is $C(\mathbb R) \subset H_{s}^{loc}$ (localized Sobolev space)?

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