Geodesic
Holmgren problem for elliptic equation with singular coefficients
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 32 (2020) no. 3, pp. 114-126

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In the present work, we investigate the Holmgren problem for an multidimensional elliptic equation with several singular coefficients. We use a fundamental solution of the equation, containing Lauricella's hypergeometric function in many variables. Then using an «abc» method, the uniqueness for the solution of the Holmgren problem is proved. Applying a method of Green's function, we are able to find the solution of the problem in an explicit form. Moreover, decomposition and summation formulae, formulae of differentiation and some adjacent relations for Lauricella's hypergeometric functions in many variables were used in order to find the explicit solution for the formulated problem.
Keywords: Holmgren problem, multidimensional elliptic equations with several singular coefficients, summation formula, Lauricella hypergeometric function in many variables, Green's function.
Mots-clés : decomposition formula 
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     author = {T. G. Ergashev and A. Hasanov},
     title = {Holmgren problem for elliptic equation with singular coefficients},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {114--126},
     publisher = {mathdoc},
     volume = {32},
     number = {3},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2020_32_3_a8/}
}
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T. G. Ergashev; A. Hasanov. Holmgren problem for elliptic equation with singular coefficients. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 32 (2020) no. 3, pp. 114-126. http://geodesic.mathdoc.fr/item/VKAM_2020_32_3_a8/