A minimizing principle for the Poisson-Boltzmann equation
  The Poisson-Boltzmann equation is often presented via a variational formulation based on the electrostatic potential. However, the functional has the defect of being non-convex. It can not be used as a local minimization principle while coupled to other dynamic degrees of freedom. We formulate a convex dual functional which is numerically equivalent at its minimum and which is more suited to local optimization. 
A.C. Maggs
cond-mat.soft cond-mat.stat-mech physics.comp-ph