- #1
Combinatorics
- 36
- 5
Homework Statement
Given a positive subharmonic function [itex] u[/itex] , defined on [itex]R^2 [/itex], how can I prove that [itex] u[ /itex] must be constant?
Homework Equations
[itex] \Delta u \leq 0 [/itex] is the definition of subharmonic function !
The Attempt at a Solution
I've tried solving this by using a new function [itex] v_\epsilon = u+ \epsilon log(\sqrt{x^2+y^2 } ) [/itex] , and then messing out with this [itex] /epsilon [/itex], but without any success.
Hope you'll be able to help !
Thanks !