A new theoretical approach has been developed in order to describe various
Laplacian transfer phenomena towards irregular interfaces: stationary
diffusion through semi-permeable membranes, electric transport towards
non blocking electrodes (in an electrolyte), heterogeneous catalysis on
porous surfaces. The influence of an irregular geometry, crucial for
these phenomena, can be fully taken into account using a mathematical
operator called Dirichlet-to-Neumann operator. Its spectral properties,
completely determining the linear response of the system in question,
has been studied numerically and experimentally for different prefractal
boundaries.