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Solvability of boundary singular integral operators of elasticity on surfaces with conic points

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A system of boundary singular integral equations of the linear isotropic elasticity is studied in the case where the double layer potential is generated by the stress operator. These equations are considered on a bounded two-dimensional surface without boundary which is smooth outside a finite number of conical points. The solvability of the system is proved in various weighted spaces of differentiable functions. We obtain a representation of the inverse operator of the system in terms of the inverse operators of some boundary value problems. We also obtain pointwise estimates for the kernel of this operator and “quasilocal” estimates for solutions of the integral equations in question. Bibliography: 12 titles.

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References

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Authors and Affiliations

  1. Department of Mathematical Sciences, M&O Building, University of Liverpool, Liverpool, L69 7ZL, UK

    N. V. Grachev & V. G. Maz’ya

  2. Department of Mathematics, Linköping University, SE-581 83, Linköping, Sweden

    N. V. Grachev & V. G. Maz’ya

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  1. N. V. Grachev
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  2. V. G. Maz’ya
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Correspondence to V. G. Maz’ya.

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Translated from Problemy Matematicheskogo Analiza 70, May 2013, pp. 71–84.

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Grachev, N.V., Maz’ya, V.G. Solvability of boundary singular integral operators of elasticity on surfaces with conic points. J Math Sci 191, 178–192 (2013). https://doi.org/10.1007/s10958-013-1311-z

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  • DOI: https://doi.org/10.1007/s10958-013-1311-z

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