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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
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