Limit distribution function of inhomogeneities in regions with random boundary. I

A study is made of the interaction of systems of charged particles with a membrane consisting of inhomogeneities randomly distributed in accordance with the same law in the neighborhoods of corresponding sites of a planar crystal lattice. A system of equations for the self-consistent potential $U_1(x,\xi^0,\dots,\xi^N,\dots)$ and density of surface charges $\sigma(x,\xi^0,\dots,\xi^N,\dots)$ is derived and solved.