1. The problem statement, all variables and given/known data Let u be harmonic on the bounded region A and continuous on cl(A). Then show that u takes its minimum only on bd(A) unless u is constant. 2. Relevant equations incase you are used to diffrent notation, cl(a) is clousure bd(A) is boundary 3. The attempt at a solution By the global maximum principle we have that (let m denote the minimum of u on bd(A)) (i)u(x,y) >= m for (x,y) in A (ii) if u(x,y)=m for some (x,y) in A, then u is constant. Assume u is not constant. then we have that u(x,y)>m. I dont know where to go from here. I think i still need to show that the only possible place it can take its min is on bd(A). but i have no clue how to do that.