Timeline for Modulus of continuity of the Dirichlet Laplacian problem
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 2, 2017 at 1:40 | comment | added | user97743 | I think we shoud ask: what are properties of the domain in which the modulus of continuity of the solution <= C x the modulus of continuity of the boundary data? | |
| Jan 31, 2017 at 22:41 | comment | added | Pietro Majer | So a modified question could be: what moduli of continuity for $\phi$ admit solutions with the same m.of (times a constant). | |
| Jan 31, 2017 at 22:34 | comment | added | Pietro Majer | In fact, following my hints above you just get a mod of cont. $\omega'$ for the solution, but it is not dominated by $\omega$... | |
| Jan 31, 2017 at 22:12 | comment | added | user97743 | Sadly, after searching online, I 've learned that this is not correct even $\Omega $ is a ball. | |
| Jan 29, 2017 at 10:16 | comment | added | user97743 | Can u give some more hints. The right hand side is proportional to $\omega_{\varphi}$, not just depending on $\omega_{\varphi}$. | |
| Jan 29, 2017 at 9:02 | comment | added | Pietro Majer | When bounding $|u(y)-u(x)|$ you can reduce to the case $x\in\partial\Omega$ by the maximum principle, and then $y\in\partial\Omega$ too, via a supersolution (here should appear C). | |
| Jan 29, 2017 at 6:35 | history | edited | user97743 | CC BY-SA 3.0 |
added 1 character in body
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| Jan 28, 2017 at 23:06 | history | asked | user97743 | CC BY-SA 3.0 |