Geodesic
Third double-layer potential for a generalized bi-axially symmetric Helmholtz equation
Ufa mathematical journal, Tome 10 (2018) no. 4, pp. 111-121

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The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in studying this potential, the properties of the fundamental solutions of the given equation are used. At present, all fundamental solutions to the generalized bi-axially symmetric Helmholtz equation are known but nevertheless, only for the first of them the potential theory was constructed. In this paper we study the double layer potential corresponding to the third fundamental solution. By using properties of Appell hypergeometric functions of two variables, we prove limiting theorems and derive integral equations involving the density of double-layer potentials in their kernels.
Keywords: generalized bi-axially symmetric Helmholtz equation, Green formula, fundamental solution, third double-layer potential, Appell hypergeometric functions of two variables, integral equations with a density of double-layer potential in their kernel. 
@article{UFA_2018_10_4_a10,
     author = {T. G. Ergashev},
     title = {Third double-layer potential for a generalized bi-axially symmetric {Helmholtz} equation},
     journal = {Ufa mathematical journal},
     pages = {111--121},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2018_10_4_a10/}
}
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T. G. Ergashev. Third double-layer potential for a generalized bi-axially symmetric Helmholtz equation. Ufa mathematical journal, Tome 10 (2018) no. 4, pp. 111-121. http://geodesic.mathdoc.fr/item/UFA_2018_10_4_a10/