Geodesic
Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator
Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 47-59

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

Degenerating elliptic equations containing the Bessel operator are mathematical models of axial and multi-axial symmetry of a wide variety of processes and phenomena of the surrounding world. Difficulties in the study of such equations are associated, inter alia, with the presence of singularities in the coefficients. This article considers a $p$-dimensional, $p\geqslant3,$ degenerating elliptic equation with a negative parameter, in which the Bessel operator acts on one of the variables. A fundamental solution of this equation is constructed and its properties are investigated, in particular, the behavior at infinity and at points of the coordinate planes $x_{p-1}=0,$ $x_p=0.$ The results obtained will find application in the construction of solutions of boundary value problems, since on the basis of a fundamental solution, it is possible to choose the potential with which the singular problem is reduced to a regular system of integral equations.
Keywords: degenerating elliptic equation with a Bessel operator; degenerating B-elliptic equation; fundamental solution. 
@article{VTAMU_2019_24_125_a4,
     author = {N. A. Ibragimova},
     title = {Construction of a fundamental solution for a one degenerating elliptic equation with a {Bessel} operator},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {47--59},
     publisher = {mathdoc},
     volume = {24},
     number = {125},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a4/}
}
TY  - JOUR
AU  - N. A. Ibragimova
TI  - Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2019
SP  - 47
EP  - 59
VL  - 24
IS  - 125
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a4/
LA  - ru
ID  - VTAMU_2019_24_125_a4
ER  - 
%0 Journal Article
%A N. A. Ibragimova
%T Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator
%J Vestnik rossijskih universitetov. Matematika
%D 2019
%P 47-59
%V 24
%N 125
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a4/
%G ru
%F VTAMU_2019_24_125_a4
N. A. Ibragimova. Construction of a fundamental solution for a one degenerating elliptic equation with a Bessel operator. Vestnik rossijskih universitetov. Matematika, Tome 24 (2019) no. 125, pp. 47-59. http://geodesic.mathdoc.fr/item/VTAMU_2019_24_125_a4/