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arXiv · 2110.03084

On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations

Gerard Awanou·Gantumur Tsogtgerel
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Abstract

We prove that two Aleksandrov solutions of a generated prescribed Jacobian equation have the same gradients at points where they are both differentiable. For the optimal transportation case where two solutions can be translated to agree at a point without changing the $g$-subdifferential at that point, we recover the uniqueness up to a constant of solutions. For the general case, our result is a new proof with less regularity assumptions of a key theorem recently used to prove the uniqueness of solutions.

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Gerard Awanou, Gantumur Tsogtgerel. 2021-10-06. On uniqueness of weak solutions to the second boundary value problem for generated prescribed Jacobian equations. https://arxiv.org/abs/2110.03084

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