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Sep 5, 2023 at 7:56 answer added ViktorStein timeline score: 0
Jun 15, 2020 at 7:27 history edited CommunityBot
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Mar 21, 2019 at 11:13 history edited vicubso CC BY-SA 4.0
A grammar error (Used "¿" to begin a question).
Mar 21, 2019 at 9:06 comment added vicubso @NikWeaver That is what i though initially. I suppose that's what he's thinking about, the only thing that sounded a bit odd to me was the words he uses... every convex function is continuous and hence lower semicontinuous as Piotr Hajlasz pointed out. If that is what he is trying to say, I wonder why he tries to emphasise the lower semicontinuity.
Mar 20, 2019 at 16:35 comment added Nik Weaver Thanks for the paper. I notice that we are soon considering $g(u,v)$ where $u$ and $v$ are functions in $L^p(\Omega)$. Maybe he is really thinking of the lower semicontinuous and convex envelope of the function $v \mapsto g(u,v)$?
Mar 20, 2019 at 14:05 comment added Mahdi - Free Palestine @PiotrHajlasz: Also, It is possible that Ambrosio refers to biconjugate of a function, see en.wikipedia.org/wiki/Convex_conjugate#Biconjugate.
Mar 20, 2019 at 13:00 comment added Piotr Hajlasz A convex function on $\mathbb{R}^n$ is always continuous. In fact it is locally Lipschitz continuous so why talking about lower semicontinuity? I believe this might be because Ambrosio refers to a general fact that the convex envelope of a lower semicontinuous function on a compact convex set is lower semicontinuous, see math.stackexchange.com/q/2221026. But I am not sure.
Mar 20, 2019 at 12:09 comment added Nik Weaver I'll look at the paper as soon as I get a chance, but my immediate thought is, might he mean "for each $s$ the convex envelope of $g(s,\cdot)$" (which is lower semicontinous in $s$)?
Mar 20, 2019 at 11:20 review First posts
Mar 20, 2019 at 11:24
Mar 20, 2019 at 11:18 history asked vicubso CC BY-SA 4.0