Timeline for Reference request: PDE of the form $(\Delta - |u|^2)f = F(u)$
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2020 at 12:16 | comment | added | Leo Moos | @Jakob: Have you checked the books of Han-Lin or Gilbarg-Trudinger for an answer to your question? Off the top of my head, the answer to your question might depend on whether $u \in L^p$ for some $p > n$. Could you be more precise about the specific estimate you are looking for? I also think there might be a typo in the inequality you state, should it be $\lVert f \rVert \leq C \lVert F(u) \rVert$? | |
| Nov 2, 2020 at 13:07 | comment | added | Jakob Möller | @LeoMoos I know it is linear but I need to know how to estimate the RHS (say $|u|^2$ is known to be in some $L^p$ for $1\leq p \leq \infty$ in terms of the LHS. The usual Hardy-Littlewood-Sobolev inequality doesn't apply here, right? | |
| Oct 30, 2020 at 12:15 | comment | added | leo monsaingeon | Looks very linear to me indeed! | |
| Oct 30, 2020 at 10:33 | comment | added | Leo Moos | I'm a bit confused: seeing as $u$ is given, isn't this just a linear PDE? | |
| Oct 30, 2020 at 9:40 | history | asked | Jakob Möller | CC BY-SA 4.0 |