Timeline for Finding super(sub)-harmonic functions for an elliptic operator
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2020 at 7:03 | vote | accept | sharpe | ||
| Sep 9, 2020 at 16:46 | answer | added | Mohan Ramachandran | timeline score: 2 | |
| Sep 9, 2020 at 15:10 | comment | added | Giorgio Metafune | Yes, exactly. The same you wrote | |
| Sep 9, 2020 at 14:35 | comment | added | sharpe | @GiorgioMetafune Thank you for letting me know. $f=\alpha^{-1}(1-|x|^2)^{\alpha}$ ? This seems to be the simplest. | |
| Sep 9, 2020 at 13:17 | comment | added | Giorgio Metafune | I find $Lf=\left(4(1-c/2-\alpha)r^2+2cx\cdot \theta +2n (1-r^2)\right )(1-r^2)^{\alpha-1}$. Then $(4-4\alpha -2c)r^2+2cx\cdot \theta +2n (1-r^2) \ge (4-4\alpha -2c)r^2-2rc|\theta|+2n (1-r^2)$ and this last expressione is nonegative if $c(1+|\theta|) <2$, choosing $\alpha$ small as you did. | |
| Sep 9, 2020 at 12:51 | comment | added | sharpe | @GiorgioMetafune Your result is consistent with the case of $\theta=0$. | |
| Sep 9, 2020 at 11:31 | comment | added | sharpe | @GiorgioMetafune I don't find it. Could you tell me the reason? | |
| Sep 9, 2020 at 7:12 | comment | added | Giorgio Metafune | It seems that your barrier works if $c(1+|\theta|) <2$; do you find the same? | |
| Sep 9, 2020 at 1:51 | history | edited | sharpe | CC BY-SA 4.0 |
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| Sep 8, 2020 at 13:10 | history | edited | sharpe | CC BY-SA 4.0 |
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| Sep 8, 2020 at 12:56 | comment | added | sharpe | @GiorgioMetafune Thank you for your comment. There will be no function satisfying the conditions if $c \ge 2$ and $\theta=0$. This is based on probabilistic considerations. | |
| Sep 8, 2020 at 12:35 | comment | added | Giorgio Metafune | Do you know what happens if $\theta=0$ and $c\geq 2$? | |
| Sep 8, 2020 at 7:19 | history | edited | sharpe | CC BY-SA 4.0 |
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| Sep 8, 2020 at 5:47 | history | edited | sharpe | CC BY-SA 4.0 |
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| Sep 8, 2020 at 5:38 | history | edited | sharpe | CC BY-SA 4.0 |
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| Sep 8, 2020 at 5:06 | history | asked | sharpe | CC BY-SA 4.0 |