Timeline for Sign changing elliptic problem
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 4, 2022 at 20:16 | comment | added | username | Weyl Law is proved by comparison estimation see these notes or others, it's the first link in google. If you have an estimate on $u_m$ you can follow the same steps and derive the corresponding estimate for your problem? | |
| Jul 4, 2022 at 8:10 | comment | added | Math604 | Thanks for the comment. Ya I don't know anything about Weyl's Law. It sounds like you are saying that $T_m:= \inf \{ | \mu_{k,m}|: k \ge 1 \} \rightarrow 0$ as $ m \rightarrow 0$; which is what I was mainly interested in. Any hope of trying to find a bound on how quick it approaches zero? | |
| Jul 3, 2022 at 21:15 | comment | added | username | What about Weyl's Law? Since $\mu_{,k,m}\to+\infty$ with $k$, you are asking, for large $m$, about the asymptotic distribution of the eigenvalues, since the minimum for a fixed, large, $m$ will be attained for some large $k$. If you are asking for an inf on $k$ and $m$, it looks like it should be zero, for that reason, since eigenvalues become close together ($N=3$, so $2/N<1$). | |
| Jul 3, 2022 at 19:21 | history | asked | Math604 | CC BY-SA 4.0 |