All Questions
2 questions
1
vote
1
answer
242
views
Subharmonic function in unbounded regions
The harmonic majorization for a subharmonic function $h$ is well-known for bounded regions $\Omega \subset \mathbb{C}$:
$$h \le 0 \text{ in }\partial \Omega \Longrightarrow h \le 0 \text{ in }\Omega.$$...
- 91.8k
25
votes
1
answer
2k
views
The origin of Discrete `Liouville's theorem'
It is known that discrete Liouville's theorem for harmonic functions on $\mathbb{Z}^2$ was proved by Heilbronn (On discrete harmonic functions. - Proc. Camb. Philos. Soc. , 1949, 45, 194-206).
If ...
- 188k