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On the Asymptotic Behavior of Solutions of a System of Integral Equations of Mixed Boundary Value Problem of Plane Elasticity in a Neighborhood of Corner Points of the Contour

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Abstract

In the papers [1–2] a method for investigation of asymptotics of solutions near singularities of the boundary of boundary integral equations, arising in problems of potential theory was proposed. This method is based on the fact that solutions of integral equations can be expressed in terms of solutions of some exterior and interior boundary value problems. In the author’s papers [3–4] asymptotics of solutions of boundary integral equations near corner points of the contour in plane problems of elasticity of the first two boundary value problems for the Lame’s system was obtained.

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References

  1. S.S. Zargaryan and V.G. Maz’ya, Singularities of the solution of the system of integral equations of potential theory, arising in Zaremba problem, Vestn. Leningrad Univ. Math, n 1 (1984). English transl. v. 16 (1984).

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  2. S.S. Zargaryan and V. Maz’ya, On the asymptotic of solutions of integral equations of potential theory in a neighborhood of corner points of the contour, Prikl. Mat. Mekh. v. 48, n 1 (1984), English transl. in Y. Appl. Math. Mech. v. 48 (1984).

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  3. S.S. Zargaryan On the asymptotic of solutions of singular integral equations of plane problem of elasticity with given external stress components on the boundary, Dokl. Akad. Nauk Arm. SSR, v. 77, n 1 (1983).

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  4. S.S. Zargaryan, Singularities of the solution of the system of singular integral equations of plane problem of elasticity with given external stress components on the boundary, Dokl. Akad. Nauk Arm. SSR, v. 77, n 4 (1983).

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  5. N.S. Kakhniashvili, Investigation of plane problems of elasticity by method of potential theory, Trudy Tbil.Univ. Mekh.Mat., v.50 (1953).

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© 1988 Plenum Press, New York

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Zargaryan, S. (1988). On the Asymptotic Behavior of Solutions of a System of Integral Equations of Mixed Boundary Value Problem of Plane Elasticity in a Neighborhood of Corner Points of the Contour. In: Král, J., Lukeš, J., Netuka, I., Veselý, J. (eds) Potential Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0981-9_44

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  • DOI: https://doi.org/10.1007/978-1-4613-0981-9_44

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8276-1

  • Online ISBN: 978-1-4613-0981-9

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