List questions from bochner-spaces

Published on 02 Apr 2016 - 16:32

1.1k

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Integral of a weak derivative

Published on 03 Apr 2016 - 18:39

2k

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$L^{2}(0,T; L^{2}(\Omega))=L^{2}([0,T]\times\Omega)$?

Published on 15 May 2013 - 9:43

719

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$C_0^\infty(0,T)\cdot V$ dense in the Bochner space $L^2(0,T;V)$

Published on 06 Oct 2013 - 15:41

49

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$\langle f, u \rangle = 0$ for all $u \in C_c^\infty(0,T;H)$ implies $f=0$? Please check proof

Published on 07 Oct 2013 - 12:18

189

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Existence of solutions to linear evolution equation with a noncoercive operator

Published on 23 Oct 2013 - 9:08

389

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Exchangability of inner product and integral in bochner spaces

Published on 29 Oct 2013 - 12:59

130

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The space $C^1([0,T]\times \Omega)$ for $\Omega$ open and bounded

Published on 14 Dec 2013 - 18:05

433

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Measurability of composition (Bochner function)

Published on 15 Jan 2014 - 22:15

98

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For a PDE $u' + Au = f$, if $f$ and $u'$ are smooth does it mean $Au$ is also smooth?

Published on 26 Feb 2014 - 15:46

148

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An equality that holds with $v_t \in L^2(0,T;L^2(\Omega))$ but its proof requires $v_t \in L^2(0,T;H^1(\Omega))$

Published on 27 Feb 2014 - 21:25

112

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If $u_m \rightharpoonup u$, how to show using monotonicity that $f(u_m) \rightharpoonup f(u)$?

Published on 06 Mar 2014 - 14:39

181

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Bounding $\int_0^T\int_\Omega v|\nabla u|^2$ given that $v \in L^2(0,T;L^2(\Omega))$ and $u \in L^2(0,T;H^1(\Omega)) \cap L^\infty(0,T;L^2(\Omega))$?

Published on 07 Mar 2014 - 11:03

229

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Don't understand proof of a PDE argument, author uses $w(t,\cdot) \in L^6(\Omega)$ when $w(t,\cdot) \in H^1(\Omega)$.

Published on 08 Mar 2014 - 22:22

172

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A regularity result for a parabolic PDE? Want $u' \in L^\infty((0,T)\times \Omega)$

Published on 09 Mar 2014 - 15:42

List Question

Strong measurability - simpler solution?

Integral of a weak derivative

$L^{2}(0,T; L^{2}(\Omega))=L^{2}([0,T]\times\Omega)$?

$C_0^\infty(0,T)\cdot V$ dense in the Bochner space $L^2(0,T;V)$

$\langle f, u \rangle = 0$ for all $u \in C_c^\infty(0,T;H)$ implies $f=0$? Please check proof

Existence of solutions to linear evolution equation with a noncoercive operator

Exchangability of inner product and integral in bochner spaces

The space $C^1([0,T]\times \Omega)$ for $\Omega$ open and bounded

Measurability of composition (Bochner function)

For a PDE $u' + Au = f$, if $f$ and $u'$ are smooth does it mean $Au$ is also smooth?

An equality that holds with $v_t \in L^2(0,T;L^2(\Omega))$ but its proof requires $v_t \in L^2(0,T;H^1(\Omega))$

If $u_m \rightharpoonup u$, how to show using monotonicity that $f(u_m) \rightharpoonup f(u)$?

Bounding $\int_0^T\int_\Omega v|\nabla u|^2$ given that $v \in L^2(0,T;L^2(\Omega))$ and $u \in L^2(0,T;H^1(\Omega)) \cap L^\infty(0,T;L^2(\Omega))$?

Don't understand proof of a PDE argument, author uses $w(t,\cdot) \in L^6(\Omega)$ when $w(t,\cdot) \in H^1(\Omega)$.

A regularity result for a parabolic PDE? Want $u' \in L^\infty((0,T)\times \Omega)$

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