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arXiv · 2603.24457

Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Amp\`ere Equation with Slow Perturbation Term

Kui Yan·Jiguang Bao
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Abstract

In this paper, we obtain optimal asymptotic behavior of parabolically convex $C^{2,1}$ solution to the parabolic Monge-Amp\`ere equation $-u_t\det D_x^2u=f$, where $f$ converges to $1$ at infinity with a slow rate. This result extends the elliptic estimate in \cite{lb5} to the parabolic setting.

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Kui Yan, Jiguang Bao. 2026-03-25. Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Amp\`ere Equation with Slow Perturbation Term. https://arxiv.org/abs/2603.24457

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