Timeline for Finding a critical point on a product of two balls under some boundary conditions
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 20, 2016 at 11:48 | history | bounty ended | CommunityBot | ||
| Sep 17, 2016 at 21:49 | vote | accept | aglearner | ||
| Sep 14, 2016 at 19:39 | comment | added | Jaap Eldering | My feeling is that there always exists a critical point, because you have directions along $x$ where $f$ increases and along $y$ where it decreases. This creates some kind of saddle configuration, that I think should always contain a critical point. Maybe Morse theory or some adaptation of the (finite-dimensional) mountain pass lemma may help you here, but I don't know these topics well. | |
| Sep 13, 2016 at 21:10 | comment | added | aglearner | Thanks Jaap! Indeed this looks like a counterexample. Do you think you can elaborate this example further so that $F$ does not have any critical point in $[-1,1]\times (-1,1)$? | |
| Sep 13, 2016 at 16:19 | history | answered | Jaap Eldering | CC BY-SA 3.0 |