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Sibirskii Matematicheskii Zhurnal, 2003, Volume 44, Number 1, Pages 3–20 (Mi smj1165)  
This article is cited in 14 scientific papers (total in 14 papers)

The Cauchy problem for second-order elliptic systems on the plane

È. V. Arbuzov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Full-text PDF (271 kB) Citations (14)
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Abstract: Regular solutions to second-order elliptic systems on the plane are representable in terms of $A$-analytic functions satisfying an operator equation of the Beltrami type. We prove Carleman-type formulas for reconstruction of solutions from data on a part of the boundary of the domain. We use these formulas for solving the Cauchy problems for the system of Lame equations, the Navier–Stokes system, and the system of equations of elasticity with resilience.
Keywords: second-order elliptic system, Cauchy problem, Carleman formula, $A$-analytic function.
Received: 04.11.2002
English version:
Siberian Mathematical Journal, 2003, Volume 44, Issue 1, Pages 1–16
DOI: https://doi.org/10.1023/A:1022034001292
Bibliographic databases:
UDC: 517.956.223
Language: Russian
Citation: È. V. Arbuzov, “The Cauchy problem for second-order elliptic systems on the plane”, Sibirsk. Mat. Zh., 44:1 (2003), 3–20; Siberian Math. J., 44:1 (2003), 1–16
Citation in format AMSBIB
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\jour Siberian Math. J.
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\pages 1--16
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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