Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Ampère Equation with Slow Perturbation Term
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912982252912640 |
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| author | Yan, Kui Bao, Jiguang |
| author_facet | Yan, Kui Bao, Jiguang |
| contents | In this paper, we obtain optimal asymptotic behavior of parabolically convex $C^{2,1}$ solution to the parabolic Monge-Ampère 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24457 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Ampère Equation with Slow Perturbation Term Yan, Kui Bao, Jiguang Analysis of PDEs 35B40, 35A01, 35K55 In this paper, we obtain optimal asymptotic behavior of parabolically convex $C^{2,1}$ solution to the parabolic Monge-Ampère 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. |
| title | Optimal Asymptotic Behavior at Infinity of Ancient Solution to the Parabolic Monge-Ampère Equation with Slow Perturbation Term |
| topic | Analysis of PDEs 35B40, 35A01, 35K55 |
| url | https://arxiv.org/abs/2603.24457 |