LINEAR DIFFERENTIAL EQUATIONS WITH HOLOMORPHIC COEFFICIENTS ON MANIFOLD WITH CUSPIDAL SINGULARITIES AND LAPLACE’S EQUATION

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Korovina, M V; Smirnov, V Y

LINEAR DIFFERENTIAL EQUATIONS WITH HOLOMORPHIC COEFFICIENTS ON MANIFOLD WITH CUSPIDAL SINGULARITIES AND LAPLACE’S EQUATION Journal Article

Mechanics, Materials Science & Engineering, 19 , 2019, ISSN: 2412-5954.

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Authors: M.V. Korovina, V.Y. Smirnov

ABSTRACT. We study the asymptotics of solutions of partial differential equations with higher degenerations. Such equations arise, for example, when studying solutions of elliptic equations on manifolds with cuspidal singular points. We construct the asymptotics of a solution of the Laplace equation defined on a manifold with a cuspidal singularity of order k.

Keywords:linear differential equations, holomorphic coefficients, cuspidal singularities, Laplace’s equation

DOI 10.2412/mmse.2.82.53

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