Solve: Δu=-1, u(1, theta)=sin(theta). 0<r<1, -pie<theta<pie, u finite at r=0 What I've done: u=u1+u2. Δu2=0, with u(1, theta)=sin(theta). So eventually u2=rsin(theta). The u1 problem however I am not sure how to solve. Eigenfunction expansion doesnt seem like it would work (though not exactly sure why, if so). Help?