Electron. J. Differential Equations, Vol. 2018 (2018), No. 100, pp. 1-12.

Fundamental solutions of two multidimensional elliptic equations

Ilnur Garipov, Rinat Mavlyaviev

We construct fundamental solutions for two-multidimensional elliptic equations. The solutions are written in explicit form via hypergeometric Gauss functions for $\lambda=0$ and via confluent Horn functions for $\lambda\neq 0$. It is proved that the fundamental solutions found possess power-type singularity $\rho^{2-n}$ as $\rho\to 0$.

Submitted December 4, 2017. Published April 28, 2018.
Math Subject Classifications: 35A08.
Key Words: Fundamental solution; hypergeometric Gauss function; confluent Horn function; transmutation operator.

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Ilnur Garipov
Kazan (Volga region) Federal University
Kazan, Russia
email: ilnur_garipov@mail.ru
Rinat Mavlyaviev
Kazan (Volga region) Federal University
Kazan, Russia
email: mavly72@mail.ru

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