Abstract:
Sufficient conditions on a function continuous on the unit circle are found ensuring that the solution of the Dirichlet problem in the unit disk for a certain second order partial differential equation with this boundary function is a homeomorphism of the unit disk onto a simply connected Jordan domain.
Key words and phrases:
elliptic operator, unit disk, Dirichlet problem, one-to-one mapping.
Citation:
A. B. Zaitsev, “On the univalence of solutions of second order elliptic equations in the unit disk on the plane”, Investigations on linear operators and function theory. Part 43, Zap. Nauchn. Sem. POMI, 434, POMI, St. Petersburg, 2015, 91–100; J. Math. Sci. (N. Y.), 215:5 (2016), 601–607
\Bibitem{Zai15}
\by A.~B.~Zaitsev
\paper On the univalence of solutions of second order elliptic equations in the unit disk on the plane
\inbook Investigations on linear operators and function theory. Part~43
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 434
\pages 91--100
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6144}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3493702}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 215
\issue 5
\pages 601--607
\crossref{https://doi.org/10.1007/s10958-016-2866-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84965032101}
Linking options:
https://www.mathnet.ru/eng/znsl6144
https://www.mathnet.ru/eng/znsl/v434/p91
This publication is cited in the following 5 articles:
Astamur Bagapsh, Alexandre Soldatov, “On the Solution of the Dirichlet Problem for Second-Order Elliptic Systems in the Unit Disk”, Mathematics, 11:20 (2023), 4360
A.O. Bagapsh, “Some Analytic and Geometric Properties of Solution to Skew-Symmetric Elliptic Systems”, HoBMSTU.SNS, 2021, no. 1 (94), 4
A. B. Zaitsev, “On the maximum principle for solutions of second order elliptic equations”, Russian Math. (Iz. VUZ), 64:8 (2020), 8–13
A. O. Bagapsh, “On the geometric properties of the Poisson kernel for the Lamé equation”, Comput. Math. Math. Phys., 59:12 (2019), 2124–2144
A. B. Zaitsev, “On the mappings of plane domains by solutions to second order elliptic equations”, Russian Math. (Iz. VUZ), 62:8 (2018), 22–26
Citation in format AMSBIB
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