Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes

A boundary value problem for Laplace’s equation in a bounded domain with two small holes is considered. Third-type boundary conditions are set on the boundaries of the holes. A Neumann condition is specified on the outer boundary of the domain. A uniform asymptotic approximation of the solution is constructed and justified up to an arbitrary power of a small parameter.