Timeline for Boundary value of Sobolev space
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27 at 18:19 | answer | added | TaQ | timeline score: 1 | |
| Jul 26 at 14:20 | comment | added | TaQ | I do not agree with Aleksei Kulikov's view that a negative answer could be obtained by some "functional analysis mumbo-jumbo". Instead, it seems to me that either there should be an explicit counterexample or a proof of the positive result. I tried some "tilted cone" like functions with one finite jump discontinuity point at the boundary, but these examples failed basically because computing $\int_\Omega|\nabla u|^2$ lead to the implication $\int_0^1t^{-\frac32}{\rm\,d\,}t=+\infty\Rightarrow\int_\Omega|\nabla u|^2=+\infty\,$. | |
| Jul 26 at 11:42 | answer | added | gerw | timeline score: 0 | |
| Jul 20 at 17:51 | comment | added | Aleksei Kulikov | It shouldn't be true if the embedding from $H_0^1(D)\to C(D)$ is not continuous by some functional analysis mumbo-jumbo, which I'm pretty sure it isn't even when $D$ is a disk, but I'll leave it to someone else to figure out the details. | |
| Jul 20 at 17:41 | history | asked | Focus | CC BY-SA 4.0 |