Geodesic
Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 48-57

Voir la notice de l'article provenant de la source Math-Net.Ru

The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. These fundamental solutions are directly connected with multiple hypergeometric functions and the decomposition formula is required for their investigation which would express the multivariable hypergeometric function in terms of products of several simpler hypergeometric functions involving fewer variables. In this paper, such a formula is proved instead of a previously existing recurrence formula.The order of singularity and other properties of the fundamental solutions that are necessary for solving boundary value problems for degenerate second-order elliptic equations are determined.
Keywords: multidimensional elliptic equation with several singular coefficients, fundamental solutions
Mots-clés : decomposition formula. 
@article{JSFU_2020_13_1_a3,
     author = {Tuhtasin G. Ergashev},
     title = {Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {48--57},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a3/}
}
TY  - JOUR
AU  - Tuhtasin G. Ergashev
TI  - Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 48
EP  - 57
VL  - 13
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a3/
LA  - en
ID  - JSFU_2020_13_1_a3
ER  - 
%0 Journal Article
%A Tuhtasin G. Ergashev
%T Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 48-57
%V 13
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a3/
%G en
%F JSFU_2020_13_1_a3
Tuhtasin G. Ergashev. Fundamental solutions for a class of multidimensional elliptic equations with several singular coefficients. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 1, pp. 48-57. http://geodesic.mathdoc.fr/item/JSFU_2020_13_1_a3/