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Jun 22, 2023 at 13:49 comment added Iosif Pinelis @GuyFsone : Essentially the same example, with $u(x_1,x_2,\dots,x_d)=\sqrt n\,1(0<x_1<1/n,0<x_2<1,\dots,0<x_d<1)$, works for any $d$.
Jun 22, 2023 at 13:28 comment added Guy Fsone I acknowledge this counter example works. I forgot to mention that d>q.I encountered this problem in the context of Sobolev embedding. Sorry for the inconvenience.
Jun 22, 2023 at 11:21 history answered Fedor Petrov CC BY-SA 4.0