Timeline for Strong solution to $u_t - \Delta_p u = f$
Current License: CC BY-SA 3.0
7 events
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| Feb 2, 2015 at 11:42 | history | edited | Joonas Ilmavirta |
Added p-laplace tag.
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| Jan 12, 2015 at 9:36 | comment | added | Juhana Siljander | I assume you mean the test functions to be time-dependent. If $f \equiv 0$, then $\partial_t u \in L^p$, if I remember correctly. I suspect something similar is true even more generally with non-zero, but smooth enough, $f$. The reference for this result is, however, very difficult to find. I think there is a note by Peter Lindqvist (NTNU) in some journal of the Norwegian Academy or something like that. | |
| Nov 25, 2014 at 17:52 | comment | added | jamesC | @TommiBrander thanks for the comment. I am not really familiar with optimal regularity but maybe that is an alternative approach. | |
| Nov 25, 2014 at 11:11 | comment | added | Tommi | I am not familiar with the p-heat equation, but for the stationary p-Laplace equation the best classical regularity for solutions is $C^{1,\alpha}$. The E-L equation of the energy $\int (|\nabla u|^2+\varepsilon)^{p/2}$ does hold point-wise and its solutions converge in $C^1$ to solutions of the original equation. Maybe something like this could be useful for you? | |
| Nov 25, 2014 at 10:46 | history | edited | jamesC | CC BY-SA 3.0 |
added 67 characters in body
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| Nov 25, 2014 at 10:42 | review | First posts | |||
| Nov 25, 2014 at 10:55 | |||||
| Nov 25, 2014 at 10:39 | history | asked | jamesC | CC BY-SA 3.0 |