Laplace equation Definition and 154 Threads

u(r, θ) satisfies Laplace's equation inside a 90º sector of a circular annulus with a < r < b ; 0 < θ < π/2 . Use separation of variables to find the solution that satisfies the boundary conditions u(r, 0) = 0 u(r, π/2) = f(r) ; a < r < b u(a, θ) = 0 u(b, θ) = 0 ; 0 < θ < π/2 Consider all...

I've recently started studying Laplace's equation and it's solution under various simple circumstances in electrostatics. I tried to solve the equation for a parallel plate condenser system, but I couldn't meet the boundary conditions. I had two plates, one placed on xz plane at y=0 (with...

Does \nabla ^2 u(r,\theta) = 0 with the boundary conditions u(1,\theta) = u(2,\theta) = \sin^2 \theta have any solutions? This was a problem on my exam but someone must have written the conditions wrong, or am I stupid?

Hi, I'm trying to solve the Laplace equatio in oblate and prolate spheroidal coordinates, but it's proving to be too much for me to handle, can anyone help me out? You can see the equations I'm using in: http://mathematica.no.sapo.pt/index.html