Perron method: proving maximum to be subharmonic

[4real4sure]

Hello,

I was going through Perron method within the text and came across Lemma 1 which states that if u₁,u₂ are subharmonic on some domain D and satisfies Cauchy boundary conditions (for example), then so does max(u₁,u₂). I am quite confused in terms of proving the statement. How would one theoretically explain this? Any help would be appreciated.

Thank you

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

 

[Hawkeye18]

Subharmonic functions are upper semicontinuous functions satisfying mean value inequality. If this definition is used, then the proof is quite elementary. I am nor writing it down, because it is probably what is written in your text (what text are you using?).

You can gain some intuition by looking at convex functions, convex functions of 1 real variable can be considered as subharmonic functions of one real variable.