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.

💡 Research Summary

The Poisson‑Boltzmann (PB) equation is the cornerstone of continuum electrostatics for electrolyte solutions. Traditionally it is derived from a variational functional expressed in terms of the electrostatic potential φ:

(F