Abstract:
The action of the Monge-Ampère operator on polynomials of degree four in two variables is investigated. Two necessary conditions for the Monge-Ampère equation to have a solution are established. Sufficient conditions for solvability are indicated, which coincide with necessary conditions in certain cases. Invariant submanifolds of the action of the Monge-Ampère operator are found. Closed invariant chains of polynomials are constructed, and all the fixed points having the form of general polynomials of degree four are found.
Bibliography: 9 titles.
Citation:
Yu. A. Aminov, “The action of the Monge-Ampère operator on polynomials in the plane and its fixed points of polynomial type”, Sb. Math., 210:12 (2019), 1663–1689
\Bibitem{Ami19}
\by Yu.~A.~Aminov
\paper The action of the Monge-Amp\`ere operator on polynomials in the plane and its fixed points of polynomial type
\jour Sb. Math.
\yr 2019
\vol 210
\issue 12
\pages 1663--1689
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Linking options:
https://www.mathnet.ru/eng/sm9168
https://doi.org/10.1070/SM9168
https://www.mathnet.ru/eng/sm/v210/i12/p3
This publication is cited in the following 1 articles:
Yu. A. Aminov, “Existence of polynomial solutions of degree 4 of the Monge-Ampère equation. Large deflections of thin plates”, Sb. Math., 214:8 (2023), 1051–1065
Citation in format AMSBIB
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