Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options answers only not deleted user 108637
7 votes
Accepted

Is there a harmonic function with just one singular point?

Yes, this is possible. An explicit example is $$u(x, y, z) = 1 - I_0\left(\sqrt{x^2 + y^2}\right) \, \cos z$$ when $L = \pi$, and $u\big(\frac{\pi x}{L}, \frac{\pi x}{L}, \frac{\pi x}{L}\big)$ for a g …
Daniele Tampieri's user avatar
1 vote

If the first Dirichlet eigenfunction on a set $D$ is regular up to the boundary, is $D$ regu...

One cannot expect any fatness of the domain $D$: the thinner $D$ at some boundary point, the faster the decay of the eigenfunction near this point. In particular, the first eigenfunction will be Lipsc …
Mateusz Kwaśnicki's user avatar