Timeline for What is the infinite Morse index solution?
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| when toggle format | what | by | license | comment | |
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| Sep 7, 2023 at 10:40 | comment | added | Michele Caselli | A comment on your first question: note that it might be different considering critical points of the energy and $C^2$-solutions as the Dancer-Farina paper does. Even for $3\le N \le 9$, infinite index solutions could be singular/unbounded. For example $u(x):=-2\log|x|+C_N$ is a weak solution (for some dimensional $C_N$) to $-\Delta u = e^u$ for every $N\ge 3$, but it has infinite index. Indeed, if it would have finite index then by a result of Figalli-Zhang it would be bounded and smooth, and this is not the case. | |
| Aug 31, 2023 at 2:37 | vote | accept | Elio Li | ||
| Aug 29, 2023 at 18:10 | answer | added | Otis Chodosh | timeline score: 5 | |
| Aug 29, 2023 at 16:29 | history | asked | Elio Li | CC BY-SA 4.0 |