Soliton-Stripe Patterns in Charged Langmuir Monolayers

We consider a charged Langmuir monolayer problem where electrostatic interaction forces undulations in the molecular concentration of the monolayer. Using the -convergence theory in singular perturbative variational calculus, we prove the existence of soliton-stripe lamellar patterns as one-dimensional local minimizers of the free energy, which are characterized by sharp domain walls delineating fully segregated dense liquid and dilute gas regions of the monolayer.