Localizing several potentially synchronous brain activities with low signal-to-noise ratio from ElectroEncephaloGraphic (EEG) recordings is a challenging problem. In this paper we propose a novel source localization method, named CoRE, which uses a Cosparse Representation of EEG signals. The underlying analysis operator is derived from physical laws satisfied by EEG signals, and more particularly from Poisson's equation. In addition, we show how physiological constraints on sources, leading to a given space support and fixed orientations for current dipoles, can be taken into account in the optimization scheme. Computer results, aiming at showing the feasability of the CoRE technique, illustrate its superiority in terms of estimation accuracy over dictionary-based sparse methods and subspace approaches.