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arXiv · 2406.07883

Continuity estimates for the gradient of solutions to the Monge-Ampère equation with nature boundary conditions

Huaiyu Jian·Ruixuan Zhu
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Abstract

We study the first derivative estimates for solutions to Monge-Ampère equations in terms of modulus of continuity. As a result, we establish the optimal global log-Lipschitz continuity for the gradient of solutions to the Monge-Ampère equation with natural boundary conditions.

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Huaiyu Jian, Ruixuan Zhu. 2024-06-12. Continuity estimates for the gradient of solutions to the Monge-Ampère equation with nature boundary conditions. https://arxiv.org/abs/2406.07883

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