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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.14026 |
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| _version_ | 1866911641142034432 |
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| author | Lu, Zhihao |
| author_facet | Lu, Zhihao |
| contents | We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-Émery) Ricci curvature bounded below. This answers a fundamental question that has existed for a long time. As a corollary, this provides a new proof of the Gidas-Spruck classical Liouville theorem. The Harnack inequality is also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14026 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited Lu, Zhihao Analysis of PDEs We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-Émery) Ricci curvature bounded below. This answers a fundamental question that has existed for a long time. As a corollary, this provides a new proof of the Gidas-Spruck classical Liouville theorem. The Harnack inequality is also obtained. |
| title | Logarithmic gradient estimate and Universal bounds for semilinear elliptic equations revisited |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2308.14026 |