Timeline for Strong maximum principle in entire space
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2023 at 2:57 | comment | added | Davidi Cone | @GiorgioMetafune how to guarantee that $(1+K u^{\frac{4}{n-2}}) \geq 0$ in $B\left(x_0, r\right)$? since $K$ may be always negative. | |
| Aug 13, 2023 at 19:07 | answer | added | Giorgio Metafune | timeline score: 3 | |
| Aug 12, 2023 at 3:31 | comment | added | Davidi Cone | Sorry, I just don't know how to quote your name, may be @ Giorgio Metafune like this? And I guess this may not need the sign condition of $K$ by write $K=K^{+}+K^{-}$. | |
| Aug 11, 2023 at 11:48 | comment | added | Giorgio Metafune | Please quote my name so I receive a notification, I saw your reply by chance. Sorry, I just realized that K is not a positive constant! | |
| Aug 11, 2023 at 8:12 | comment | added | Davidi Cone | I'm wondering if we do not need the sign condition of $K(x)$? | |
| Aug 10, 2023 at 21:50 | comment | added | Giorgio Metafune | I just use that a superharmonic function with a global miniminum is constant in a open connected set. No boundedness assumption on the set is needed. So, if your u is zero somewhere, since it is nonegative, it has a minimum and it is zero everywhere. | |
| Aug 10, 2023 at 14:32 | comment | added | Davidi Cone | Can you give some details about the proof, thanks. | |
| Aug 10, 2023 at 6:54 | comment | added | Giorgio Metafune | Yes, the usual proof for subharmonic/superharmonic functions works in any open connected set and gives $u=0$ if u vanishes somewhere. Or else you can use the strong minimun principle in any ball. | |
| Aug 10, 2023 at 5:30 | history | edited | Davidi Cone | CC BY-SA 4.0 |
added 4 characters in body
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| Aug 10, 2023 at 4:32 | history | edited | Davidi Cone | CC BY-SA 4.0 |
added 15 characters in body
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| Aug 10, 2023 at 4:31 | comment | added | Davidi Cone | sorry, here $u$ not equal to 0. | |
| Aug 10, 2023 at 2:57 | comment | added | Michael Renardy | Isn't u=0 a nonnegative solution? | |
| Aug 10, 2023 at 1:58 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; deleted "thanks"
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| Aug 9, 2023 at 23:12 | history | asked | Davidi Cone | CC BY-SA 4.0 |