Dear all,
In my research I need to solve a polar form of Laplace equation. No big deal, I have solved but I am not able to satisfy the boundary conditions.
For the past three months I have tried every thing but no success. I am so desperate please help me:

a: is a constant


B.C.1: U(R,t)=0 for -t1<t<t1 and R is a constant
B.C.2: (sin(t)/r)*Ut-(cos(t))*Ur=0 when r=(R-h)/cos(t) for -t1<t<t1 and h is a constant

My solution:

The first part is a general solution which since the equation is linear can be extended with a sigma and the second part having a is a particular solution.
A,B,C,D, and k should be satisfied.

Any feedback will be highly appreciated:

Amin Mohebbi
Ph.D. candidate, UNL
Nebraska- Lincoln