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Apr 30 at 8:54 vote accept HtmlProg
Apr 30 at 8:54 comment added HtmlProg Yes of course, that was rather trivial. Thanks!
Apr 30 at 7:04 comment added Kostya_I @HtmlProg we have $f_{ad,ar}-f_{ad,r}>0$ on these spheres, hence by maximum principle everywhere outside of them.
Apr 30 at 7:02 history edited Kostya_I CC BY-SA 4.0
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Apr 29 at 20:19 comment added HtmlProg Thanks, this is a nice argument! Might be a naïve question: but to show that inequality, you're saying it's since the values of $f_{ad,r}$ on spheres of radius $ar$ are smaller than the boundary values. But none of these spheres are touching the origin, so why could we obtain that inequality, specifically at the origin if we only know that the values on the spheres of radius $r$ are smaller?
Apr 29 at 8:53 history answered Kostya_I CC BY-SA 4.0