List questions from bochner-spaces

138

Views

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 15 Apr 2026 - 19:51

114

Views

Does $u=0$ a.e. in $[0,T]\times\Omega$ imply for a.a. $t \in [0,T]$, $u(t)=0$ a.e. in $\Omega$?

Published on 13 Apr 2026 - 9:27

269

Views

Sobolev spaces and using monotone convergence theorem (don't understand a paper)

Published on 12 Apr 2026 - 12:58

246

Views

Want a dense subset of a Sobolev-Bochner space!!

Published on 15 Apr 2026 - 14:30

130

Views

Mollification of functions in $L^2(0,T;H^1)\cap H^1(0,T;H^{-1})$

Published on 17 Apr 2026 - 4:20

111

Views

Weak convergence in some space.

Published on 11 Apr 2026 - 18:51

63

Views

Showing that a function is bounded in $L^1$ given a bound on its distribution function

Published on 11 Apr 2026 - 5:26

157

Views

Convergence in $L^p(0,T;L^q(\Omega))$

Published on 14 Apr 2026 - 10:13

1k

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Strong maximum principle for weak solutions?

Published on 08 Apr 2026 - 18:13

103

Views

Property of intersections of Bochner spaces

Published on 10 May 2026 - 14:06

1.1k

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Smoothing effect for weak solutions of heat equation

Published on 09 Apr 2026 - 0:00

147

Views

Equivalence of two definitions of weak solution (from a book, I don't understand something!!!!)

Published on 11 Apr 2026 - 12:42

57

Views

Measurability of $u:[0,T] \to X$ where $u$ is in Bochner space

Published on 14 Apr 2026 - 2:55

795

Views

Weak star convergence leads to weak convergence of derivative?

Published on 15 Apr 2026 - 0:13

193

Views

How to interpret dual space convergence in norm $L^2(0,T;V^*)$ (sobolev--bochner spaces)

Published on 12 Apr 2026 - 18:31

List Question

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?

Does $u=0$ a.e. in $[0,T]\times\Omega$ imply for a.a. $t \in [0,T]$, $u(t)=0$ a.e. in $\Omega$?

Sobolev spaces and using monotone convergence theorem (don't understand a paper)

Want a dense subset of a Sobolev-Bochner space!!

Mollification of functions in $L^2(0,T;H^1)\cap H^1(0,T;H^{-1})$

Weak convergence in some space.

Showing that a function is bounded in $L^1$ given a bound on its distribution function

Convergence in $L^p(0,T;L^q(\Omega))$

Strong maximum principle for weak solutions?

Property of intersections of Bochner spaces

Smoothing effect for weak solutions of heat equation

Equivalence of two definitions of weak solution (from a book, I don't understand something!!!!)

Measurability of $u:[0,T] \to X$ where $u$ is in Bochner space

Weak star convergence leads to weak convergence of derivative?

How to interpret dual space convergence in norm $L^2(0,T;V^*)$ (sobolev--bochner spaces)

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