Elliptic differential operators with degeneration of a noninteger order

Recieved: 12/12/2022

Accepted: 01/30/2023

Published: 05/31/2023

Keywords: noninteger order degeneration, analytic coefficients, elliptic equation, equation with a small parameter

To cite this article

Emel’yanov D.P. Elliptic differential operators with degeneration of a noninteger order. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2023. N 2, p.12-22 https://doi.org/10.55959/MSU/0137–0782–15–2023–47–2–12–22.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Emel’yanov D.P. (Lomonosov Moscow State University (MSU))

Abstract

Dirichlet boundary value problem for the elliptic equation in a rectangle with a noninteger degeneration and analytic coefficients is considered. Applying the method of spectral isolation of singularities, the formal solution to the problem is constructed as a series which exhibits its non-analytic dependence with respect to y at the origin. Green’s function method verifies the convergence of the series to the classical solution of the considered problem.