Timeline for While doing Lp estimates, is the constant C monotonically increasing with respect to the parameters it depends on?
Current License: CC BY-SA 4.0
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| Apr 4, 2021 at 16:06 | comment | added | Wentao Hu | @GiorgioMetafune Thank you very much! I posted this question because the validity of an outcome in my thesis depends on the monotonicity of $C$, but inspired by your comment, I find it is enough to assure the validity provided $C$ is locally bounded. I will still try to work through the proof and explicitly keep track of the constants involved as it is a great exercise, as is mentioned in the answer math.stackexchange.com/a/4088860/709713. | |
| Apr 4, 2021 at 10:29 | comment | added | Calvin Khor | This has been posted on (and recieved an Answer) on MSE math.stackexchange.com/questions/4088765/… | |
| Apr 4, 2021 at 9:51 | comment | added | Giorgio Metafune | Usually it is proved that $C$ stays bounded when $\lambda^{-1}, \Lambda, T, \|b_i\| \dots \le M$. If you define $C(M)$ as the best constant for which the estimate hold with the constraint $M$, this is increasing in $M$. | |
| Apr 4, 2021 at 9:23 | history | asked | Wentao Hu | CC BY-SA 4.0 |