UMD PDE Qualifying Exams/Aug2010PDE

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Problem 1[edit]

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 .

Solution[edit]

(a)[edit]

Test