# Boundary problem

1. Mar 29, 2009

### sara_87

1. The problem statement, all variables and given/known data
We are given the pde:
$$\partial^2{v}/\partial{r^2}$$+(1/r)$$\partial{v}/\partial{r}$$+(1/r^2)$$\partial^2{v}/\partial{\theta^2}$$=0
and we are given that a general solution is given by:
v(r,$$\theta$$)=A$$_{0}$$+B$$_{0}$$ln(r) + $$\sum{r^{n}(A_{n}cos(n\theta) + B_{n}sin(n\theta))}+\sum{(1/r^n)(C_{n}cos(n\theta)+D_{n}sin(n\theta))}$$

show that if $$\Omega$$ is a disk centered at the origin of radius r0, continuous solutions of the pde are of the type:
v(r,$$\theta$$)=A0+$$\sum{r^n(A_{n}cos(n\theta)+B_{n}sin(n\theta))}$$

2. Relevant equations

3. The attempt at a solution
i think we have to show that \sum{(1/r^n)(C_{n}cos(n\theta)+D_{n}sin(n\theta))}[/tex] and B0ln(r) are not continuous but i dont think thats right.
Any help would be very much appreciated.

Last edited: Mar 29, 2009