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Nov 10 at 14:45 comment added Giorgio Metafune @Victor You can choose balls $B(x_k, r/2)$ with the same radius $r<dist (G, \partial \Omega)$.
Nov 10 at 14:28 comment added Victor Why $k$ large enough implies that some neighborhood contains $z$? It can happens that the neighboors as $k$ gets larger are smaller and smaller always avoiding $z$
Oct 16, 2022 at 8:24 comment added User1132 Yes, that could be the case. Thank you for the clarification.
Oct 16, 2022 at 7:08 comment added Giorgio Metafune I guess they have in mind the usual statement for an increasing sequence of harmonic functions: convergence in one point yields convergence at every point and adopt the same terminology even though the assumptions are not the same. I do not know how common is this terminology however also Harnack inequality follows from the mean value....
Oct 16, 2022 at 6:52 comment added User1132 Professor I just want to clarify what is exactly the Harnack Principle they meant while writing the alternatives? As I am not able to find any such statement regarding Harnack principle so if you know any reference regarding the Harnack principle they stated it would be helpful.
Oct 16, 2022 at 2:06 vote accept User1132
Oct 15, 2022 at 20:46 history answered Giorgio Metafune CC BY-SA 4.0