Timeline for A question on minimum principle
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2021 at 19:17 | vote | accept | M. Rahmat | ||
| Apr 6, 2021 at 15:34 | history | edited | Yuval Peres | CC BY-SA 4.0 |
added 165 characters in body
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| Apr 6, 2021 at 15:32 | comment | added | Yuval Peres | @MateuszKwaśnicki You are right, of course, I will add the boundedness condition. | |
| Apr 6, 2021 at 7:20 | comment | added | Mateusz Kwaśnicki | I think the conditions that you give assert that there is no bounded (super)harmonic function which vanishes on (the regular part of) the finite boundary. But still there usually is an unbounded harmonic function. For example, for the half-space $\{x \in \mathbb R^d : x_1>0\}$ the probability of never hitting the boundary is clearly zero, but there is a harmonic function vanishing on the boundary: $u(x)=x_1$. | |
| Apr 6, 2021 at 5:22 | history | answered | Yuval Peres | CC BY-SA 4.0 |