Timeline for Decay estimates for simple elliptic equations
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2023 at 13:09 | comment | added | Giorgio Metafune | Not at the first oder approximation but it should enter the remainder. | |
| Jun 18, 2023 at 11:14 | comment | added | Davidi Cone | Thanks! But it seems $\alpha$ has no effect on the infinity property of the solution $p(r)$? | |
| Jun 16, 2023 at 7:05 | comment | added | Giorgio Metafune | I added (shortly) the case $n>3$ but I did not consider $n=2$. | |
| Jun 16, 2023 at 7:04 | history | edited | Giorgio Metafune | CC BY-SA 4.0 |
added 792 characters in body
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| Jun 16, 2023 at 5:44 | comment | added | Davidi Cone | Thanks! I also write something about it.\begin{gather*} p''(r)+\frac{n-1}{r}p'(r)=-4q, \\ (r^{n-1}p')'=r^{n-1}p''+(n-1)r^{n-2}p'=r^{n-1}(-4q),\\\int_{0}^{\rho}(s^{n-1}p(s)')'\,\mathrm{d} s=\int_{0}^{\rho}s^{n-1}(-4q(s))\,\mathrm{d}s=\rho^{n-1}p'(\rho),\\\rho^{1-n}\int_{0}^{\rho}s^{n-1}(-4q(s))\,\mathrm{d}s=p'(\rho)\Rightarrow \int_r^{\infty}\rho^{1-n}\int_{0}^{\rho}s^{n-1}(-4q(s))\,\mathrm{d}s=\int_r^{\infty}p'(\rho)\,\mathrm{d}\rho \end{gather*}but loss the information about $p(z)$ in the infinity. I also quite interesting about your details! Thanks again! | |
| Jun 15, 2023 at 20:52 | history | answered | Giorgio Metafune | CC BY-SA 4.0 |