Generalized Monge–Ampère type equation and its multidimensional exact solutions

A.A. Kosov; E.I. Semenov

doi:10.35634/vm250204

journal article Jun 20, 2025

Generalized Monge–Ampère type equation and its multidimensional exact solutions

A.A. Kosov

E.I. Semenov

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Vol. 35 No. 2 pp. 215-230 · Izhevsk Institute of Computer Science

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Abstract

Several variants of the multidimensional generalized Monge–Ampère equation are considered containing, in addition to the determinant of the Hessian matrix, also additional terms depending on the Laplace operator and the gradient of the desired function. It is proposed to construct exact solutions in the form of superposition of quadratic form and solutions of ordinary differential equations generated by the initial partial differential equation. We give a number of examples of exact solutions, both radially symmetric and anisotropic, expressed through combinations of elementary functions.

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Published: Jun 20, 2025
Vol/Issue: 35(2)
Pages: 215-230

Authors

A

A.A. Kosov

Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences (ISDCT SB RAS)

E

E.I. Semenov

Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences (ISDCT SB RAS)

Cite This Article

A.A. Kosov, E.I. Semenov (2025). Generalized Monge–Ampère type equation and its multidimensional exact solutions. Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 35(2), 215-230. https://doi.org/10.35634/vm250204

Generalized Monge–Ampère type equation and its multidimensional exact solutions

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