$($BVP vs Conformal mapping$)$ Consider the shadowed region bounded by $3$ Dirichlet boundary conditions as shown in Fig$\mathrm{.}1.$ Assume that horizontal bounding potential $V_0>0.$

$($a$)$ Find the potential by solving boundary valued problem with given coordinate.

$($b$)$ Under a conformal mapping $w=sin(\frac{z}{2})$ on shadowed region, describe the transformed region.

$($c$)$ Find the potential in transformed space. You may consider the boundary set into superpositioned two simple boundary sets and use superposition theorem.

rigi. rrodiem$4.$

Fig$2.$ Problem$5.$