  We use a conformal mapping technique to study the Laplacian transfer across a
rough interface. Natural Dirichlet or Von Neumann boundary condition are simply
read by the conformal map. Mixed boundary condition, albeit being more complex
can be efficiently treated in the conformal plane. We show in particular that
an expansion of the potential on a basis of evanescent waves in the conformal
plane allows to write a well-conditioned 1D linear system. These general
principle are illustrated by numerical results on rough interfaces.
