On the averaging of solutions of a second order elliptic equation with nonperiodic rapidly changing boundary conditions (Q1851498)

The authors study the problem on boundary averaging of a second-order elliptic equation in the case when the limiting problem has the third boundary condition or the Neumann condition on the domain boundary. By means of the methods developed in [\textit{O. A. Oleinik} and \textit{G. A. Chechkin}, Rend. Lincei: Mat. e Appl. (9) 7, No. 1, 5--15 (1996; Zbl 0876.35012)] the authors obtain estimates of the speed of convergence of the solution for the initial problem to the solution for the problem averaged in \(H'\)-norm with the use of a special cut off function.