A result concerning identifiability of the inverse problem of groundwater hydrology

The inverse problem of hydrology, namely finding the transmissivity, a, given the piezometric head, u, and source or sink term, f, is herein considered. The concept of identifiability and its links with the uniqueness of the solution of the inverse problem are studied. When u in H1( Omega ) has a piecewise continuous derivative a necessary and sufficient condition for a to be identifiable is stated and proved. Some interesting examples concerning this theorem are presented.