Timeline for Interior regularity for elliptic equations
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2013 at 7:45 | answer | added | Daniel Spector | timeline score: 0 | |
| Mar 6, 2013 at 5:40 | history | edited | Delio Mugnolo | CC BY-SA 3.0 |
improved formatting
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| Mar 5, 2013 at 5:33 | answer | added | Craig | timeline score: 1 | |
| Feb 21, 2013 at 9:14 | comment | added | Daniel Spector | I guess then the first question is what do Lions-Magenes mean by $\Delta u=f$ for $f \in L^2(\Omega)$? Likely these quantities are defined almost everywhere and so it is in some integral sense. Maybe the $C^\infty$ assumption is to do the extension and use Fourier transforms or some other technique like this on the whole space? I will look for a copy of it in the library and get back to you. | |
| Feb 21, 2013 at 8:20 | comment | added | Delio Mugnolo | I don't see how this implies $u\in H^1$ (or better) by the general PDE theory. All I am aware of is that you do have $H^1$ (indeed, usually even $H^2$) if you can apply Gauß-Green so that you can set up a variational formulation and apply Lax-Milgram. But in this case this is not possible, since we have no idea of what happens at the boundary. | |
| Feb 21, 2013 at 8:01 | comment | added | Daniel Spector | I think it should be worded differently, because if $u \in H^\frac{1}{2}$ then $u \in L^2$, and by the PDE this implies $u \in H^1$ (or better). Do you mean the fractional semi-norm of $u$ is finite, in this case? | |
| Feb 20, 2013 at 18:46 | comment | added | Delio Mugnolo | it is independent of the boundary condition, that is exactly the point. | |
| Feb 20, 2013 at 18:37 | comment | added | Daniel Spector | Do you want to add a boundary condition, or is this result independent of that? | |
| Feb 20, 2013 at 17:56 | history | edited | Delio Mugnolo | CC BY-SA 3.0 |
edited title
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| Feb 20, 2013 at 17:18 | history | asked | Delio Mugnolo | CC BY-SA 3.0 |