The inverse problems associated with these direct problems involve estimating the current sources within the volume conductor from measurements of voltages on the surface of either the head or body. Thus one would solve (3) with the boundary conditions:

The first is the Dirichlet condition, which says that one has a set of
discrete measurements of the voltage of a subset of the outer surface. The
second is the natural Neumann condition as seen before. While it doesn't
look much different than the formulation of the direct problem, the
mathematician Hadamard [14] noticed that inverse formulations
of boundary value problems (or their algebraic counterpart) were often *
ill-behaved*. He defined the conditions for * well-posed* and *
ill-posed* problems.