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.
Similar content being viewed by others
Change history
04 January 2021
An Erratum to this paper has been published: https://doi.org/10.1134/S0965542520300016
REFERENCES
I. G. Petrovskii, “On analyticity of solutions to systems of partial differential equations,” Mat. Sb. 5, 3–70 (1939).
M. I. Vishik, “On strongly elliptic systems of differential equations,” Mat. Sb. 29, 615–676 (1951).
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).
L. K. Hua, W. Lin, and C. Q. Wu, Second-Order Systems of Partial Differential Equations in the Plane (Pitman, Boston, 1985).
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).
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).
L. D. Landau and E. M. Lifshitz, Theory of Elasticity (Butterworth-Heinemann, Oxford, 1986; Nauka, Moscow, 1987).
G. C. Verchota and A. L. Vogel, “Nonsymmetric systems on nonsmooth planar domains,” Trans. Am. Math. Soc. 349 (11), 4501–4535 (1997).
M. A. Lavrent’ev and B. V. Shabat, Methods of the Theory of Functions of a Complex Variable (Nauka, Moscow, 1965) [in Russian].
A. A. Savelov, Plane Curves: Systematics, Properties, and Applications (Fizmatlit, Moscow, 1960) [in Russian].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by E. Chernokozhin
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542520090067