1. The problem statement, all variables and given/known data Hi all. I am looking at Laplace's equation on an annulus (just a circle where a < r < b, where "a" and "b" are constants). The boundaries of the annulus at r=a and r=b are kept at a certain temperature, which is theta-independent! Using my physical intuition, of course the solution to Laplace's equation n polar coordinates must be theta-independent as well. But is there a mathematical way of proving it?