Page 85 - 6637
P. 85
Supplementary Problems
Exercise 234. Find a function u(r, θ) harmonic in {2 < r < 4, 0 ≤ θ ≤ 2π},
satisfying the boundary condition u(2, θ) = 0, u(4, θ) = sin θ.
2
2
Exercise 235. Let u(x, y) be the harmonic function in D = {(x, y)| x +y < 36}
(
x, x < 0,
which satisfies on ∂D the Dirichlet boundary condition u(x, y) =
0, otherwise.
Using the separation of variables method, find the solution u in D.
81
