Potential Theory pp 351-362 | Cite as

# 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

Chapter

## 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).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 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).Google Scholar
- 5.N.S. Kakhniashvili, Investigation of plane problems of elasticity by method of potential theory, Trudy Tbil.Univ. Mekh.Mat., v.50 (1953).Google Scholar
- 6.V.G. Maz’ya, The potential theory for the Lame system in domains with piecewise smooth boundaries, Proc. of the Conference in 1982 on Partial Diff. Equations. Memoriam of I.N. VEKUA in Tbilisi, Tbilisi (1986).Google Scholar
- 7.V.A. Kondratev, Boundary value problems for elliptic equations in domains with conical or corner points, Trudy Moskov. Mat. Obshch. v. 16 (1967). English transl. in Trans.Moscow Math. Soc. v. 16 (1967).Google Scholar
- 8.M.L. Williams, Stress singularities resulting from.various boundary conditions in angular corners of plate in extension, J. Appl.Mech.,v.19, n 4 (1952).Google Scholar

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© Plenum Press, New York 1988