Timeline for A basic stability question
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 15, 2018 at 16:45 | comment | added | A random mathematician | Of course, but we also require $|\nabla u_i|>0$. So your example on unit ball will not be a counter example. What if we require $\partial \Omega$ to be connected? Then I guess there shouldn't be a trivial counter example. | |
| Aug 15, 2018 at 16:38 | comment | added | Willie Wong | The unit ball is simply connected. The annulus in $\mathbb{R}^d$ for $d \geq 3$ is also simply connected. The interval in $\mathbb{R}$ is also simply connected. | |
| Aug 15, 2018 at 15:53 | comment | added | A random mathematician | Thank you, Willie. Actually I forgot to mention that $\Omega$ is simply connected. Will there be a counter example under this assumption? | |
| Aug 15, 2018 at 13:51 | comment | added | Willie Wong | Basically: your equation fixes the direction but not the magnitude of the gradient, and the magnitude does matter. | |
| Aug 15, 2018 at 13:42 | history | edited | Willie Wong | CC BY-SA 4.0 |
added 33 characters in body
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| Aug 15, 2018 at 13:41 | history | undeleted | Willie Wong | ||
| Aug 15, 2018 at 13:41 | history | deleted | Willie Wong | via Vote | |
| Aug 15, 2018 at 13:35 | history | answered | Willie Wong | CC BY-SA 4.0 |