On the uniqueness of the surface sources of evoked potentials

The uniqueness of a surface density of sources localized inside a spatial region R and producing a given electric potential distribution in its boundary B₀ is revisited. The situation in which R is filled with various subregions, each one having a definite constant value for the electric conductivity is considered. It is argued that the knowledge of the potential in all B₀ fully determines the surface-located sources for a general class of surfaces supporting them and also a wide type of those sources. The class of surfaces can be defined as a union of an arbitrary but finite number of open or closed surfaces. The only restriction upon them is that no one of the closed surfaces contains inside it another (nesting) of the closed or open ones. The types of sources are surface charge densities and double layer (dipolar) densities for the open surfaces and more restrictively, only surface charge densities for the closed ones. A two-dimensional analytically solvable example illustrating the drastic appearance of uniqueness after arbitrarily small holes are opened in nested surfaces is discussed.