Optimal Weighted Smoothing and Asymptotics of Ancient Solutions for Fast Diffusion Equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913128725348352 |
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| author | Jiang, Xiqin Wang, Hua-Yang Xiong, Jingang |
| author_facet | Jiang, Xiqin Wang, Hua-Yang Xiong, Jingang |
| contents | We establish sharp weighted smoothing estimates for limit solutions to the Cauchy-Dirichlet problem for the fast diffusion equation on smooth bounded domains.
We demonstrate that the critical exponent governing these estimates coincides with the classical Brezis--Turner exponent known in the theory of semilinear elliptic equations.
As a primary application, we derive improved global Harnack inequalities and describe asymptotic behavior of positive ancient solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14622 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Weighted Smoothing and Asymptotics of Ancient Solutions for Fast Diffusion Equations Jiang, Xiqin Wang, Hua-Yang Xiong, Jingang Analysis of PDEs We establish sharp weighted smoothing estimates for limit solutions to the Cauchy-Dirichlet problem for the fast diffusion equation on smooth bounded domains. We demonstrate that the critical exponent governing these estimates coincides with the classical Brezis--Turner exponent known in the theory of semilinear elliptic equations. As a primary application, we derive improved global Harnack inequalities and describe asymptotic behavior of positive ancient solutions. |
| title | Optimal Weighted Smoothing and Asymptotics of Ancient Solutions for Fast Diffusion Equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.14622 |