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

doi:10.4213/sm9852e

Yuriy Akhmetovich Aminov

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

Algebra and Number Theory

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.

Need a simple solution for managing your BibTeX entries? Explore CiteDrive!

Web-based, modern reference management
Collaborate and share with fellow researchers
Integration with Overleaf
Comprehensive BibTeX/BibLaTeX support
Save articles and websites directly from your browser
Search for new articles from a database of tens of millions of references

Try out CiteDrive

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

Need a simple solution for managing your BibTeX entries? Explore CiteDrive!

More from our Archive

Modified Two-Parameter Liu Estimator for Addressing Multicollinearity in the Poisson Regression Model

Homology of transitive digraphs and discrete spaces

A remark on 0-cycles as modules over algebras of finite correspondences

Solvability of the Nevanlinna-Pick interpolation problem

Knot as a complete invariant of a Morse-Smale 3-diffeomorphism with four fixed points

Explicit deformation of the horospherical variety of type $\mathrm{G}_2$

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

On the weighted Bojanov-Chebyshev problem and the sum of translates method of Fenton

Symmetric matrices and maximal Nijenhuis pencils

Special Issue “Optimisation Models and Applications”