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On symplectic classification of effective 3-forms and Monge–Ampère equations

✍ Scribed by Bertrand Banos

Book ID
104358209
Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
175 KB
Volume
19
Category
Article
ISSN
0926-2245

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✦ Synopsis

We complete the list of normal forms for effective 3-forms with constant coefficients with respect to the natural action of symplectomorphisms in R 6 . We show that the 3-form which corresponds to the Special Lagrangian equation is among the new members of the classification. The symplectic symmetry algebras and their Cartan prolongations for these forms are computed and a local classification theorem for the corresponding Monge-Ampère equations is proved.

📜 SIMILAR VOLUMES

The Monge–Ampère equation: Various forms
The Monge–Ampère equation: Various forms and numerical solution
✍ V. Zheligovsky; O. Podvigina; U. Frisch 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 629 KB

We present three novel forms of the Monge-Ampère equation, which is used, e.g., in image processing and in reconstruction of mass transportation in the primordial Universe. The central role in this paper is played by our Fourier integral form, for which we establish positivity and sharp bound proper