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.
Mots-clés : improper double integral, boundary-value problem, Poisson equation. 
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     title = {Improper double integrals with a logarithmic kernel calculated by methods of elasticity theory},
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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. https://geodesic-test.mathdoc.fr/item/IVM_2019_7_a5/

[1] Kosterin A. V., Skvortsov E. V., “Analytical formula for integral whose kernel containing error function”, Lobachevskii J. Math., 37:3 (2016), 266–267 | DOI | MR | Zbl

[2] Dzhonson K., Mekhanika kontaktnogo vzaimodeistviya, Mir, M., 1989

[3] Kosterin A. V., Skvortsov E. V., “Filtratsionnaya konsolidatsiya pri ploskoi deformatsii uprugogo poluprostranstva”, Izv. RAN. Mekhan. zhidkosti i gaza, 2018, no. 2, 99–104 | DOI

[4] Polyanin A. D., Spravochnik po lineinym uravneniyam matematicheskoi fiziki, Fizmatlit, M., 2001