Abstract
We consider a boundary value problem for an elliptic differential equation with analytic coefficients that is degenerate in one of the variables in a rectangle. Using the method of spectral separation of singularities, a solution of this problem is constructed in the form of a Poisson series—a series in the eigenfunctions of the second-order limit linear ordinary differential operator with analytic coefficients. Estimates are obtained for the functions of the fundamental system of solutions and the Green’s functions of the sequence of boundary value problems corresponding to this operator; this enables one to weaken the previously known conditions for the convergence of the series constructed for the solution, including the case of presence of logarithmic singularities.
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This work was facilitated by the Moscow Center for Fundamental and Applied Mathematics.
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Translated by V. Potapchouck
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Emel’yanov, D.P., Lomov, I.S. Using Poisson Series in the Analytic Theory of Irregularly Degenerate Elliptic Differential Operators. Diff Equat 57, 636–653 (2021). https://doi.org/10.1134/S0012266121050086
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DOI: https://doi.org/10.1134/S0012266121050086