1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: PDE- Harmonic Functions

  1. Jul 7, 2012 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations
    [itex] \Delta u \leq 0 [/itex] is the definition of subharmonic function !

    3. 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 !
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted