Timeline for How to solve the $C^\alpha$ Poisson equation on closed Riemannian manifolds?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 23, 2012 at 2:33 | comment | added | Rafe Mazzeo | That is correct, though I guess you need to add a few details that the sequence of solutions $u_j$ which are bounded in $C^{2,\alpha}$ and convergent in $L^2$ (or, say, $C^2$) have limit which lies in $C^{2,\alpha}$. | |
| Aug 23, 2012 at 1:19 | comment | added | timur | @Rafe: Can you please have a look at my answer? I think I found a way around the density problem. | |
| Jul 29, 2012 at 3:21 | comment | added | Yuchen Liu | @YangMills: I mean roughly I use Rafe's method with a little difference: first use $L^2$-theory to find a weak solution $u$, then use Schauder estimate and continuity method to find a $C^{2,\alpha}$ solution $v$ locally, and their difference is a weak solution of $\Delta (u-v)=0$ hence $(u-v)$ is $C^\infty$. Therefore, $u$ is in $C^{2,\alpha}$. | |
| Jul 28, 2012 at 16:03 | comment | added | YangMills | what do you mean by "my answer is based on your first attempt"? | |
| Jul 28, 2012 at 2:49 | comment | added | Yuchen Liu | @Rafe Mazzeo: I think my answer is based on your first attempt: math.stackexchange.com/questions/172887/… | |
| Jul 28, 2012 at 2:46 | vote | accept | Yuchen Liu | ||
| Jul 20, 2012 at 21:09 | history | answered | Rafe Mazzeo | CC BY-SA 3.0 |