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On the structure of double layers in Poisson-Boltzmann equation

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  • We study the solutions to Poisson-Boltzmann equation for electrolytic solutions in a domain $\Omega$, surrounded by an uncharged dielectric medium. We establish existence, uniqueness and regularity of solutions and study in detail their asymptotic behaviour close to $\partial\Omega$ when a characteristic length, called the Debye length, is sufficiently small. This is a double layer with a thickness that changes from point to point along $\partial\Omega$ depending on the normal derivative of a harmonic function outside $\Omega$ and the mean curvature of $\partial\Omega$. We also provide numerical evidence of our results based on a finite elements approximation of the problem.
    Mathematics Subject Classification: Primary: 35Q35, 35J15; Secondary: 35B40.


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