On splitting up singularities of fundamental solutions to elliptic equations in ℂ2

It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental so...

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Bibliographic Details
Published in:Open mathematics (Warsaw, Poland) Poland), 2007-12, Vol.5 (4), p.733-740
Main Author: Savina, T.
Format: Article
Language:English
Subjects:
32S70
32W50
35J15
Complex Variables
Elliptic differential equations
Elliptic Equations
Elliptic functions
Fundamental Solution
Mathematical analysis
Operators (mathematics)
Singularity (mathematics)
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Summary:It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
ISSN:2391-5455
DOI:10.2478/s11533-007-0027-z