Geodesic
The solution of the basic boundary value problems for a singular elliptic equation by the method of potentials
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 5-15

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We have found fundamental solutions to a singular elliptic equation, expressed via hypergeometric functions. Using these fundamental solutions, we have built the simple and double layer potentials. We have reduced the basic boundary value problems for a singular elliptic equation to the equivalent Fredholm integral equations of the second kind and proved their solvability.
Keywords: fundamental solutions, simple and double layer potentials, boundary value problems, Fredholm integral equations, generalized shift operator. 
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     author = {R. M. Askhatov},
     title = {The solution of the basic boundary value problems for a~singular elliptic equation by the method of potentials},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {5--15},
     publisher = {mathdoc},
     volume = {155},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a0/}
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R. M. Askhatov. The solution of the basic boundary value problems for a singular elliptic equation by the method of potentials. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 155 (2013) no. 4, pp. 5-15. http://geodesic.mathdoc.fr/item/UZKU_2013_155_4_a0/