Timeline for Elliptic Dirichlet BVP's for regions with multiple boundary components
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2018 at 16:32 | comment | added | user126920 | For unique continuation, you need the functions to agree on an open set, and the boundary of $B_1$ isn't open. | |
| Aug 30, 2018 at 13:19 | comment | added | Rohil Prasad | Ah, my mistake. A unique continuation argument will not hold because the derivatives of two solutions with the same prescribed boundary values will not necessarily agree to infinite order at the boundary - in the case of $u = 0$ and $u = \log(|z|)$, their derivatives with respect to the normal coordinate are different. Is this correct? | |
| Aug 30, 2018 at 4:37 | comment | added | user126920 | Be careful. Your claim about the annulus would imply that $u\equiv 0$ is the only harmonic function in $B_1 \setminus B_{1/2}$ with $u=0$ on $\partial B_1$, but consider $u(z) = \log(|z|)$. | |
| Aug 30, 2018 at 2:39 | history | asked | Rohil Prasad | CC BY-SA 4.0 |