Quick question on boundary conditions:

One of the problems the Prof assigned had these boundary conditions (laplace equation in polar coord):$$v(r,\theta)=0$$$$v(r,\alpha)=0$$$$v(1,\theta)=f(\theta)$$v continuous

I'm confused on what to do with the fourth "v continuous" condition.

Question

Quick question on boundary conditions:

One of the problems the Prof assigned had these boundary conditions (laplace equation in polar coord):$$v(r,\theta)=0$$$$v(r,\alpha)=0$$$$v(1,\theta)=f(\theta)$$v continuous

I'm confused on what to do with the fourth "v continuous" condition.

anonymous · Answer

what is your equation?

anonymous · Answer

The laplace equation in polar coordinates is:

$$v_{rr}+\frac{1}{r}v_r+\frac{1}{r^2}v_{\theta \theta}=0$$

anonymous · Answer

if u want to solve it with 'separation of variables' method i think u will come up with something like this:

$ v(r,\theta )=(A r^k+Br^{-k}) (C \cos k \theta+ D  \cos k \theta ) $

u see this answer have a critical point at r=0 but v is continuous so u must let B=0

anonymous · Answer

Not sure how he wants us to solve it, we started fourier transform today, but I happened to miss class >.< Could that possibly tie in here somwhere?

anonymous · Answer

nope... i think its not connected with fourier transform...