Geodesic
Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 65-71

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The aim of this paper is to calculate some improper double integrals. We consider the plane deformation of an elastic half-space under the action of load applied to its surface. It is shown that a well-known expressions for one of the normal stresses can be represented in another form containing a definite improper triple integral with a logarithmic kernel. We give examples of calculating the triple integral for specific loads. As a result, five improper double integrals are expressed in terms of elementary functions.
Keywords: improper double integral, boundary-value problem
Mots-clés : Poisson equation. 
@article{IVM_2019_7_a5,
     author = {E. V. Skvortsov and T. V. Nikonenkova},
     title = {Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {65--71},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a5/}
}
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E. V. Skvortsov; T. V. Nikonenkova. Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 65-71. http://geodesic.mathdoc.fr/item/IVM_2019_7_a5/