Electric monopoles are indeed compatible with Maxwell equations.
Claude Bédard and Alain Destexhe

Journal of Neurophysiology 109: 1683, 2013.

Copy of the full paper (PDF)
This commentary was written in reply to the commentary of Gratiy SL, Pettersen KH, Einevoll GT, Dale AM. Pitfalls in the interpretation of multielectrode data: on the infeasibility of the neuronal current-source monopoles. J Neurophysiol 109:1681-1682, 2013.

In this commentary, the authors argued that electric monopoles are not possible in neurons and are incompatible with Maxwell equations of electromagnetism when applied to biological cells. Our reply that this is only true because an approximated version of Maxwell equations is used in biological media, where the displacement current is considered negligible. When the displacement current is allowed to be non-zero, electric monopoles are indeed possible in neurons, and are perfectly compatible with the non-approximated version of Maxwell equations.

See also previous commentary:

Destexhe, A. and Bedard, C. Do neurons generate monopolar current sources? J. Neurophysiol. 108: 953-955, 2012 (PDF copy).