Timeline for Is there any "extra regularity" to the solution to Poisson's equation posed on a 3-dimensional polyhedron?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 29, 2017 at 14:59 | vote | accept | fred | ||
| Nov 29, 2017 at 8:54 | comment | added | Hannes | @fred We are in fact working on a generalization of the results in the paper to even more nonsmooth settings by abstract interpolation principles. In case of pure Neumann boundary, there will not be an improvement, though; but if you are interested, feel free to send me an eMail (I will update my profile.. ;)). | |
| Nov 29, 2017 at 8:48 | answer | added | Hannes | timeline score: 3 | |
| Nov 28, 2017 at 18:11 | comment | added | fred | @Hannes, I am working on understanding the proof to understand if I can extend it to the pure Neumann case. I would gladly accept your answer. | |
| Nov 28, 2017 at 14:39 | comment | added | Hannes | I think the pure Neumann case is excluded (although I couldn't find the precise point where it explicitly is) because the differential operator is not coercive on the Sobolev space if there is not a small Dirichlet part of the boundary: the operator lacks the classical "$+1$" or "$+u$", or the space lacks a condition which exludes constant functions other than the constant zero function, such as the mean over $\Omega$ as you posed it. I would expect this to be a more or less straightforward modification, though. If this is still helpful to you, I'll happily post the answer of course. | |
| Nov 22, 2017 at 14:09 | comment | added | fred | @Hannes Are you familiar with the paper? Do you know if there is any reason why Theorem 1 couldn't be extended to the pure Nuemann case? | |
| Nov 22, 2017 at 13:59 | comment | added | fred | @Hannes Your suggestion was exactly what I needed. I wouldn't have found it without you. What I asked for is pretty much exactly theorem 1 in that paper. If you want to write an answer to this I will accept your answer. Thank You! | |
| Nov 21, 2017 at 14:36 | comment | added | Hannes | Maybe this paper could also be useful. | |
| Nov 21, 2017 at 14:19 | comment | added | Willie Wong | Maz'ya and Rossman's Elliptic equations in polyhedral domains seems promising, and may be more digestible than the original papers. | |
| Nov 21, 2017 at 14:00 | history | asked | fred | CC BY-SA 3.0 |