On permeable potential boundary conditions for the Laplace–Beltrami operator

Under study are the so-called permeable potential boundary conditions for the Laplace–Beltrami operator defined in a domain Ω on the unit sphere S in ℝ 3 . The permeability of boundary conditions means that a solution to a boundary value problem in Ω coincides with a solution to the Laplace–Beltrami equation on the whole sphere in absence of any boundary conditions.