6 Let u be a C 2 () C() solution to the elliptic equation a(x, y)uxx + b(x, y)uyy = 0, in a bounded domain R 2 . Here a, b are continuous positive functions in . Prove that max u = max u. Hint: Consider the auxiliary function w(x, y) = u(x, y) + ((x x) 2 + (y y) 2 ) where (x, y) is some fixed point, and > 0. Show that u(x, y) max u + C0,(x, y) , where C0 > 0 is independent of