UMD PDE Qualifying Exams/Aug2010PDE

Problem 1Edit

A superharmonic   satisfies   in  , where here   is open, bounded.

(a) Show that if   is superharmonic, then

 .

(b) Prove that if   is superharmonic, then  

(c) Suppose   is connected. Show that if there exists   such that   then   is constant in  .

SolutionEdit

(a)Edit

Test