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- W2136676876 abstract "We consider an equation $$ L_{alpha ,beta ,gamma} (u) equiv u_{xx} + u_{yy} + u_{zz} + displaystyle frac{{2alpha}}{x}u_x + displaystyle frac{{2beta}}{y}u_y + displaystyle frac{{2gamma}}{z}u_z = 0 $$ in a domain ${bf R}_3^ + equiv {{({x,y,z}): x > 0, y > 0, z > 0}}$. Here $alpha ,beta ,gamma$ are constants, moreover $0 < 2alpha, 2beta, 2gamma < 1$. Main result of this paper is a construction of eight fundamental solutions for above-given equation in an explicit form. They are expressed by Lauricella's hypergeometric functions with three variables. Using expansion of Lauricella's hypergeometric function by products of Gauss's hypergeometric functions, it is proved that the found solutions have a singularity of the order $1/r$ at $r to 0$." @default.
- W2136676876 created "2016-06-24" @default.
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- W2136676876 date "2009-01-05" @default.
- W2136676876 modified "2023-09-27" @default.
- W2136676876 title "Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients" @default.
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