Timeline for Where to locate $0\in \Omega$ to get $u_{\varepsilon}(0)\neq 0$ where $\Delta u_{\varepsilon} + (\lambda-\varepsilon) u_{\varepsilon} = \frac{1}{|x|}$

15 events

when toggle format	what		by	license	comment
Sep 9, 2021 at 12:00	comment	added	username		It is an interesting question. It is probably easier to address for very large $k$. A strategy could be : a/ show that $u$ must cancel within the domain. b/ consider the problem on the connected set near the boundary where $u isn't zero. c/ use Hopf's Lemma, which has a somewhat quantitative version.
S Jul 13, 2021 at 14:47	history	suggested	username		added a tag
Jul 13, 2021 at 10:04	review	Suggested edits
S Jul 13, 2021 at 14:47
Jul 9, 2021 at 21:03	history	edited	Jonas	CC BY-SA 4.0	added 105 characters in body
Jul 7, 2021 at 14:03	history	edited	Jonas		edited tags
Jul 7, 2021 at 13:52	history	edited	Jonas	CC BY-SA 4.0	added 14 characters in body
Jul 5, 2021 at 9:56	history	edited	Jonas	CC BY-SA 4.0	added 2 characters in body
Jul 4, 2021 at 13:57	history	edited	Jonas	CC BY-SA 4.0	edited body
Jul 4, 2021 at 13:50	history	edited	Jonas	CC BY-SA 4.0	added 19 characters in body
Jul 4, 2021 at 12:27	history	edited	Jonas	CC BY-SA 4.0	added 1 character in body
Jul 4, 2021 at 12:07	history	edited	Jonas	CC BY-SA 4.0	added 532 characters in body
Jul 4, 2021 at 11:49	history	edited	Jonas	CC BY-SA 4.0	added 917 characters in body
Jul 4, 2021 at 11:41	history	edited	Jonas	CC BY-SA 4.0	added 917 characters in body
Jul 4, 2021 at 2:18	history	edited	Jonas	CC BY-SA 4.0	added 7 characters in body
Jul 4, 2021 at 1:57	history	asked	Jonas	CC BY-SA 4.0