This article is cited in 1 paper

Existence of polynomial solutions of degree 4 of the Monge-Ampère equation. Large deflections of thin plates

Yu. A. Aminov<sup>ab

a</sup> B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine
^b Brasília, Brazil

Abstract: We provide necessary and sufficient conditions for the solvability of a simplest Monge-Ampère equation, assuming that both the right-hand side and the solution are polynomials of degree 4. We give a constructive method of solution of the basic system of algebraic equations corresponding to the Monge-Ampère operator under the above conditions on the prescribed polynomial. Applications to large deflections of thin plates are presented.
Bibliography: 9 titles.

Keywords: five-dimensional space, polynomial, algebraic invariant, solvability, mapping, thin plate, Airy function, deflection.

MSC: 35C11, 35G20

Received: 24.10.2022 and 30.04.2023

DOI: 10.4213/sm9852

 English version: Sbornik: Mathematics, 2023, 214:8, 1051–1065

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