Geodesic
Solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 5-14

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Fundamental solutions to a degenerate elliptic equation are found. Using these fundamental solutions, simple and double layer potentials are built. The basic boundary value problems for a degenerate elliptic equation are reduced to the equivalent Fredholm integral equations of the second kind. Their solvability is proved.
Keywords: degenerate elliptic equation, method of potentials, double layer potential, simple layer potential, Fredholm equation, generalized translation operator. 
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     title = {Solution of the basic boundary value problems for a~degenerate elliptic equation by the method of potentials},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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R. M. Askhatov; R. N. Abaydullin. Solution of the basic boundary value problems for a degenerate elliptic equation by the method of potentials. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 157 (2015) no. 1, pp. 5-14. http://geodesic.mathdoc.fr/item/UZKU_2015_157_1_a0/