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

Kui Yan; Jiguang Bao

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

Analysis of PDEs 2026-03-26 v1

Authors: Kui Yan , Jiguang Bao

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.

Keywords

parabolic Monge-Ampere equation asymptotic behavior slow perturbation convex solutions infinite behavior

Cite

@article{arxiv.2603.24457,
  title  = {Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Amp\`ere Equation with Slow Perturbation Term},
  author = {Kui Yan and Jiguang Bao},
  journal= {arXiv preprint arXiv:2603.24457},
  year   = {2026}
}

Comments

14 pages

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