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Research Article | Open Access

Weak solutions of generated Jacobian equations

School of Mathematics and Shing-Tung Yau Center of Southeast University, Southeast University, Nanjing 211189, China
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Abstract

We prove two groups of relationships for weak solutions to generated Jacobian equations under proper assumptions on the generating functions and the domains, which are generalizations for the optimal transportation case and the standard Monge-Ampère case respectively. One group of weak solutions is Aleksandrov solution, Brenier solution and C-viscosity solution. The other group of weak solutions is Trudinger solution and L p -viscosity solution.

Keywords

generated Jacobian equationsAleksandrov solutionsBrenier solutionsC-viscosity solutionsTrudinger solutionsLp-viscosity solutions

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Mathematics in Engineering
Volume 5 Issue 3,
June 2023
Pages 1-20
DOI: 10.3934/mine.2023064

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Cite this article:
Jiang F. Weak solutions of generated Jacobian equations. Mathematics in Engineering, 2023, 5(3): 1-20. https://doi.org/10.3934/mine.2023064

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Received: 20 April 2022
Revised: 27 October 2022
Accepted: 20 November 2022
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)