1. The problem statement, all variables and given/known data Let u(x; y) be real, nonconstant, and continuous in a closed bounded region R. Let u(x; y) be harmonic in the interior of R. Prove that the maximum and minimum value of u(x; y) in this region occurs on the boundary. 2. Relevant equations the theorem said that( a function analtic in bounded domain and continous up to and including its boundry attains its maximum modlus on the boundry 3. The attempt at a solution can i suppose that u(x;y) is nonzero ?