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On Solutions of Elliptic Systems with a Jump at the Boundary

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Abstract

The Dirichlet problem for a strongly elliptic system of the second order with constant coefficients in the domain with a piecewise smooth boundary and piecewise continuous boundary data is considered. The behavior near the jump point of the boundary function is shown.

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  • 04 January 2021

    An Erratum to this paper has been published: https://doi.org/10.1134/S0965542520300016

REFERENCES

  1. I. G. Petrovskii, “On analyticity of solutions to systems of partial differential equations,” Mat. Sb. 5, 3–70 (1939).

    Google Scholar 

  2. M. I. Vishik, “On strongly elliptic systems of differential equations,” Mat. Sb. 29, 615–676 (1951).

    MathSciNet  Google Scholar 

  3. L. K. Hua, W. Lin, and C. Q. Wu, “On the uniqueness of the solution of the Dirichlet problem of the elliptic system of differential equations,” Acta Math. Sinica 15 (2) (1965).

  4. L. K. Hua, W. Lin, and C. Q. Wu, Second-Order Systems of Partial Differential Equations in the Plane (Pitman, Boston, 1985).

    Google Scholar 

  5. A. O. Bagapsh and K. Yu. Fedorovskiy, “C 1-approximation of functions by solutions of second-order elliptic systems on compact sets in \({{\mathbb{R}}^{2}}\),” Proc. Steklov Inst. Math. 298, 35–50 (2017).

    Article  MathSciNet  Google Scholar 

  6. A. V. Bitsadze, “On the uniqueness of the solution to the Dirichlet problem for elliptic partial differential equations,” Usp. Mat. Nauk 3 (6), 211–212 (1948).

    MathSciNet  Google Scholar 

  7. L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Butterworth-Heinemann, Oxford, 1986; Nauka, Moscow, 1987).

  8. G. C. Verchota and A. L. Vogel, “Nonsymmetric systems on nonsmooth planar domains,” Trans. Am. Math. Soc. 349 (11), 4501–4535 (1997).

    Article  MathSciNet  Google Scholar 

  9. M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  10. A. A. Savelov, Plane Curves: Systematics, Properties, and Applications (Fizmatlit, Moscow, 1960) [in Russian].

    Google Scholar 

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ACKNOWLEDGMENTS

I am grateful to V.I. Vlasov for helpful advice when preparing this article.

Funding

This work was supported by the Russian Foundation for Basic Research, project no. 17-11-01064-P.

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Correspondence to A. O. Bagapsh.

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Translated by E. Chernokozhin

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Bagapsh, A.O. On Solutions of Elliptic Systems with a Jump at the Boundary. Comput. Math. and Math. Phys. 60, 1445–1451 (2020). https://doi.org/10.1134/S0965542520090067

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