On splitting up singularities of fundamental solutions to elliptic equations in \(\mathbb C^{2}\).

*(English)*Zbl 1145.35308Summary: 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 \(\mathbb C^{2}\). In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.

##### MSC:

35A20 | Analyticity in context of PDEs |

35A08 | Fundamental solutions to PDEs |

32S70 | Other operations on complex singularities |

35J15 | Second-order elliptic equations |

32W50 | Other partial differential equations of complex analysis in several variables |

35C15 | Integral representations of solutions to PDEs |

##### Keywords:

complex variables; elliptic equations; fundamental solution; analytic coefficients; singularities on characteristics
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\textit{T. V. Savina}, Cent. Eur. J. Math. 5, No. 4, 733--740 (2007; Zbl 1145.35308)

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##### References:

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