(lap) means the Laplacian
Vrr means the second derivative of V with respect to r
V(theta theta) means the second derivative of V with respect to theta
Solve:
(lap)V(r,theta)= Vrr+(1/r)Vr+(1/r^2)V(theta theta)=0
0 < r < 1, -(pi) < theta < pi
V(1,theta) = {1, -(pi/2) < theta < (pi/2)
{0, elsewhere
Please show all work including the derivation of any eigenvalues or eigenvectors.
Thank you
This shows how to solve an elliptic boundary value problem with Laplace and polar coordinates