On the Solvability of Maxwell's Equations
  Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the fields is an oscillating electric dipole. As before it is found that the fields calculated by different methods are at variance. In addition, the reason for the discrepancies is revealed: The retarded integrals turn out not to satisfy the inhomogeneous wave equations which they are supposed to solve. 
Wolfgang Engelhardt
physics.gen-ph