Timeline for Approximation of "endpoint" initial data for the 3D wave equation
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Oct 21, 2020 at 17:51 | comment | added | Capublanca | I think you are right, thank you for the comment. I had some doubts cause if $f_{n} $ are the mollifications we don't have that they converge to $f$ in $L^{\infty}$, but for the uniform boundedness they seem to be sufficient. | |
| Oct 21, 2020 at 17:37 | comment | added | Willie Wong | Couldn't you just mollify? Convolution with a spatial approximation to identity commutes with solving the wave equation (it is linear). And convolution decreases the $L^\infty$ norm. | |
| Oct 21, 2020 at 16:47 | comment | added | Capublanca | Yes Willie, exactly. | |
| Oct 21, 2020 at 16:40 | comment | added | Willie Wong | Just to clarify: you know $f\in L^2$ such that $A_f \in L^2L^\infty$, and you want approximations $f_n\in H^2$, converging to $f$ in $L^2$, such that $A_n \in L^2L^\infty$ is uniformly bounded? | |
| Oct 21, 2020 at 16:28 | history | asked | Capublanca | CC BY-SA 4.0 |