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Mar 31, 2016 at 19:20 comment added Higgs-Boson thanks a lot for all of your answers. I know the point in this question.
Mar 31, 2016 at 15:18 comment added Christian Remling @AlexandreEremenko: Well, I tried it with a Poisson kernel first (which fits my description better), but that's too singular after squaring, so switched to a logarithm then... :)
Mar 31, 2016 at 2:39 comment added Alexandre Eremenko Sure. BTW the description in your comment better describes the example in my answer:-)
Mar 31, 2016 at 2:35 comment added Christian Remling @AlexandreEremenko: Yes, but I think what I do is natural, too: solve the Dirchlet problem on a thin rectangle with a boundary value that is large only on a small portion of the boundary and check if the area average of $u^2$ can stay bounded.
Mar 31, 2016 at 2:30 comment added Alexandre Eremenko An easy way to see that his inequality cannot be correct is just by scaling: if you multiply all his functions on constants, sup norms multiply on the same constants, but the integral of the square on the square of the constant.
Mar 30, 2016 at 23:14 history undeleted Christian Remling
Mar 30, 2016 at 23:14 history edited Christian Remling CC BY-SA 3.0
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Mar 30, 2016 at 22:02 history edited Christian Remling CC BY-SA 3.0
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Mar 30, 2016 at 20:28 history deleted Christian Remling via Vote
Mar 30, 2016 at 20:27 history answered Christian Remling CC BY-SA 3.0