In the elasticity theory, plasma theory, and the theory of multidimensional diffusion processes, some phenomena can be described by boundary value problems for elliptic functional differential equations that associate boundary points with inner points. This nonlocal effect leads to the appearance of singularities inside the domain. The paper is devoted to an elliptic partial differential equation containing contracted and expanded arguments of the higher derivatives of the unknown function. A priori estimates of generalized solutions are obtained in weighted spaces. © 2017 EDP Sciences.