Construction of Exact Solutions of Irregularly Degenerate Elliptic Equations with Analytic Coefficients

We solve a boundary value problem (problem E in the sense of M.V. Keldysh) for an irregularly degenerate elliptic operator in a rectangle. The exact solution of the problem is constructed as a series in the eigenfunctions of the limit operator. The method of spectral isolation of singularities, whic...

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Bibliographic Details
Published in:Differential equations 2019, Vol.55 (1), p.46-59
Main Authors: Emel’yanov, D. P., Lomov, I. S.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We solve a boundary value problem (problem E in the sense of M.V. Keldysh) for an irregularly degenerate elliptic operator in a rectangle. The exact solution of the problem is constructed as a series in the eigenfunctions of the limit operator. The method of spectral isolation of singularities, which generalizes the method of regularization of singular perturbations to the case of degenerate elliptic equations, is developed.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266119010051