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Sep 26, 2022 at 23:03 comment added Mateusz Kwaśnicki @AlexandreEremenko: Sure thing! This is what I meant by "solutions of both problems are pretty much the same".
Sep 26, 2022 at 19:21 history edited Alexandre Eremenko CC BY-SA 4.0
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Sep 26, 2022 at 19:16 comment added Alexandre Eremenko @Mateusz Kwasnicki: the question was that the "ends" are "not felt", or "felt little". I quantified it.
Sep 26, 2022 at 17:28 comment added Mateusz Kwaśnicki If I understand correctly, this answer is kind of orthogonal to the question. :-) You seem to be assuming zero boundary condition on the side of the cylinder $\partial D \times [-L,L]$ and Dirichlet boundary condition prescribed by $\phi$ on the bases. The original question asks for Dirichlet boundary condition given by $\varphi$ on the side, and Neumann boundary condition on the bases. That said, solutions of both problems are pretty much the same.
Sep 26, 2022 at 17:04 history answered Alexandre Eremenko CC BY-SA 4.0