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The Method of Spectral Separation of Variables for Degenerating Elliptic Differential Operators

The Method of Spectral Separation of Variables for Degenerating Elliptic Differential Operators Differential Equations, Vol. 38, No. 6, 2002, pp. 839–846. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 6, 2002, pp. 795–801. Original Russian Text Copyright c 2002 by Lomov. PARTIAL DIFFERENTIAL EQUATIONS The Method of Spectral Separation of Variables for Degenerating Elliptic Di erential Operators I. S. Lomov Moscow State University, Moscow, Russia Received December 5, 2000 The classical Cauchy{Kowalewski theorem guarantees the local analyticity of a solution of a linear di erential equation in normal form provided that the coecients, the right-hand side, and the initial data are analytic. Investigations of degenerating elliptic equations (e.g., see [1]) showed that in this case, the analyticity of coecients of an equation is inherited by a solution. A fun- damental system consists of functions each of which is a product of a function holomorphic in a neighborhood of a degeneration point (plane) by a function that can have a singularity on the above-mentioned set. This singularity is either power-law (in this case, the exponent can be derived from the coecients of the equation), or power-law and logarithmic. Usually, the solvability of a boundary value problem for a degenerate equation is proved with the use of implicit methods for constructing the solution (for http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The Method of Spectral Separation of Variables for Degenerating Elliptic Differential Operators

Lomov, I.
Differential Equations , Volume 38 (6) – Oct 10, 2004
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Publisher
Springer Journals
Copyright
Copyright © 2002 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1020314413292
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 38, No. 6, 2002, pp. 839–846. Translated from Differentsial'nye Uravneniya, Vol. 38, No. 6, 2002, pp. 795–801. Original Russian Text Copyright c 2002 by Lomov. PARTIAL DIFFERENTIAL EQUATIONS The Method of Spectral Separation of Variables for Degenerating Elliptic Di erential Operators I. S. Lomov Moscow State University, Moscow, Russia Received December 5, 2000 The classical Cauchy{Kowalewski theorem guarantees the local analyticity of a solution of a linear di erential equation in normal form provided that the coecients, the right-hand side, and the initial data are analytic. Investigations of degenerating elliptic equations (e.g., see [1]) showed that in this case, the analyticity of coecients of an equation is inherited by a solution. A fun- damental system consists of functions each of which is a product of a function holomorphic in a neighborhood of a degeneration point (plane) by a function that can have a singularity on the above-mentioned set. This singularity is either power-law (in this case, the exponent can be derived from the coecients of the equation), or power-law and logarithmic. Usually, the solvability of a boundary value problem for a degenerate equation is proved with the use of implicit methods for constructing the solution (for

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Differential Equations – Springer Journals

Published: Oct 10, 2004

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