# Maximum principle

my function is u(x,y) = xy(x2 - y2 + 2).

Using the fact that this fxn is harmonic, how do I find the max of u on [0,1]x[0,1]?

HallsofIvy
Homework Helper
Well, do you know the theorem that says if a function is harmonic on a set, then any extreme values must occur on the boundary of the set?

The boundary of [0,1]x[0,1] consists of 4 line segments but the function, reduced to those segments, is still harmonic so any extreme values must occur at the endpoints of those segments.

so I guess the max would have to be at (1,1) then. So would i just let u(x,y) = u(1,1) and use the value that comes out?

HallsofIvy