# Using conform transformations to solve a Dirichlet problem with 3 border conditions

1. Nov 23, 2009

### libelec

1. The problem statement, all variables and given/known data

Find a function H in C such that $${\nabla ^2}H = 0$$ for y>0, H(0,y) = 1 for y<-$$/pi$$, H(0,y) = 0 for y>$$/pi$$ and H(0,y) = -1 for -$$/pi$$<y<$$/pi$$.

3. The attempt at a solution

I haven't been able to came up with anything. All the conform transformations that I know allow me to solve the Dirichlet problem with only 2 conditions, or 3 but with two of them with the same value. I was told that I could just leave the geometry of the problem like it is (that is, not make any transformation) and propose the solution A$$\theta$$1 + B$$\theta$$2 + C, being $$\theta$$1 the argument of [z - (0 -i*Pi)] and $$\theta$$2 the argument of [z - (0 +i*Pi)], but the solution I find doesn't satisfy the border conditions.

Any ideas?

2. Nov 26, 2009

### libelec

Re: Using conform transformations to solve a Dirichlet problem with 3 border conditio

Nobody knows this?

3. Nov 29, 2009

### libelec

Re: Using conform transformations to solve a Dirichlet problem with 3 border conditio

I leave a graphic of the problem.
http://img692.imageshack.us/img692/333/asdasdxk.png [Broken]

Does anybody know the answer? Because I kind of need it urgently...

Thanks.

Last edited by a moderator: May 4, 2017