n this talk, I will first recall a mean field approximation of electrostatic free energy for an ionic solution, and discuss two issues: (1) Rigorous mathematical justification of the existence of equilibrium concentrations and their Boltzmann relations; (2) The effect of inhomogeneous Dirichlet boundary condition to the solution of the related Poisson-Boltzmann equation for the electrostatic potential. I will then consider a class of variational implicit solvent models for the solvation of biomolecules, and present a formal derivation of the first variation of the electrostatic free energy with respect to the location change of the dielectric boundary. This result is needed for level-set relaxation and force calculations of biomolecular structures and dynamics. http://www.math.ucsd.edu/~bli/research/MBBseminar/