Geodesic
Existence of polynomial solutions of degree 4 of the Monge-Ampère equation. Large deflections of thin plates
Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1051-1065 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, solvability, mapping, thin plate, Airy function, deflection.
Mots-clés : polynomial, algebraic invariant 
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Yu. A. Aminov. Existence of polynomial solutions of degree 4 of the Monge-Ampère equation. Large deflections of thin plates. Sbornik. Mathematics, Tome 214 (2023) no. 8, pp. 1051-1065. http://geodesic.mathdoc.fr/item/SM_2023_214_8_a0/

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