Timeline for Recovering full regularity by energy method in the heat equation
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jul 31, 2012 at 6:44 | comment | added | timur | @Terry: Thanks a lot! It was very helpful. | |
| Jul 31, 2012 at 6:26 | comment | added | Terry Tao | I think the energy method is proving something slightly different, namely that $F \in L^2_t H^1_x$ implies $u \in L^\infty_t H^2_x$. Note that the energy method can certainly get the right fixed-time $H^s_x \to H^2_x$ bounds for the homogeneous heat propagator $e^{t\Delta}$, at which point Duhamel finishes the job; but it appears to be crucial that the energy method is applied to a homogeneous component of the solution rather than the solution itself. | |
| Jul 30, 2012 at 20:00 | history | asked | timur | CC BY-SA 3.0 |