Timeline for Dirichlet problem for manifold, how to prove $W^{1,2}_0(\Omega)$ solution is $C^{2,\alpha}(\bar{\Omega})$?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2019 at 14:39 | answer | added | Ryan Unger | timeline score: 4 | |
| Jul 16, 2019 at 14:07 | comment | added | Ryan Unger | @DCM If I recall correctly, this is what is done in Gilbarg-Trudinger. The existence theorem in Schauder theory is by continuity, so one needs to start with an existence theorem for the Laplacian. The best way to get this seems to be to pass through the $L^2$ theory. | |
| Jun 23, 2019 at 12:43 | comment | added | DCM | Going via the $L^2$/Sobolev theory seems a bit odd to me (temporarily 'forgetting' that $f$is $C^\alpha$ seems silly); I'd have thought one could stick to Holder space estimates here. Maybe I am wrong though. | |
| Jun 21, 2019 at 10:04 | history | asked | mathmetricgeometry | CC BY-SA 4.0 |