Timeline for Lower semicontinuity of a Bochner integral of a convex function
Current License: CC BY-SA 3.0
8 events
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| Jun 11, 2014 at 16:07 | comment | added | k3thomps | You are right. $f$ is only locally Lipshitz. That's OK though. We only care that $f$ is Lipshitz around $0$. I am brushing some details aside, but we are thinking of $u-v$ as being close to 0. Of course this is in the $L^2(0,T;L^2)$ sense, but with some fidling this is enough. | |
| Jun 11, 2014 at 15:33 | vote | accept | aca888 | ||
| Jun 11, 2014 at 15:28 | comment | added | aca888 | One last thing: is it obvious that the Lipschitz constant is independent of $x \in \Omega$ and $t$? When $f:[a,b] \to \mathbb{R}$ then (I believe) the Lipschitz constant depends on $b$. | |
| Jun 11, 2014 at 15:03 | comment | added | k3thomps | Oh, you are right. We didn't need the second line. Furthermore, what I had before was nonsense. My face is red. | |
| Jun 11, 2014 at 15:03 | history | edited | k3thomps | CC BY-SA 3.0 |
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| Jun 11, 2014 at 14:51 | comment | added | aca888 | Thanks. How did you get your first displayed equation? I could only get $f(\frac u2) -\frac 12f(\frac v2) \leq \frac 12f(\frac{2u-v}{2})$? Well I guess we don't need that second line anyway. | |
| Jun 11, 2014 at 14:36 | history | edited | k3thomps | CC BY-SA 3.0 |
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| Jun 11, 2014 at 14:27 | history | answered | k3thomps | CC BY-SA 3.0 |