Timeline for Higher regularity of solutions for Laplace equation with mixed boundary condition
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 24, 2018 at 13:38 | comment | added | Julienne Franz | Your comment is of great help. I just found out from Grivard's book that an $H^2$ regularity cannot be expected in my problem, at least for the mixed Dirichlet-Neumann (or Dirichlet-Robin) case. | |
| May 24, 2018 at 9:20 | comment | added | Hannes | Then you would have a mixed Neumann-Robin problem where Neumann- and Robin boundary conditions meet. I am, to be honest, not too sure how the Robin boundary data is affected by the counterexample I mentioned, but I suspect that some trickery is possible to relate the Robin boundary conditions to Neumann ones. (That's why I thought it might be helpful, but more of a comment.) In this sense, your then modified Neumann-Robin problem would be a bit more friendly, but please do not quote me on that :-) | |
| May 24, 2018 at 4:42 | comment | added | Julienne Franz | Thank you for your comment. Does this mean that, regardless of the regularity of the domain and the data, there is no hope of getting an $H^2$ regularity for the given problem. What happens when the Dirichlet data on $\Gamma_{o1}$ is replaced by a Neumann data? | |
| May 23, 2018 at 11:52 | history | answered | Hannes | CC BY-SA 4.0 |