A quantitative second order estimate for (weighted) $p$-harmonic functions in manifolds under curvature-dimension condition
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914714952400896 |
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| author | Liu, Jiayin Zhang, Shijin Zhou, Yuan |
| author_facet | Liu, Jiayin Zhang, Shijin Zhou, Yuan |
| contents | We build up a quantitative second order Sobolev estimate of $ \ln w$ for positive $p$-harmonic functions $w$ in Riemannian manifolds under Ricci curvature bounded from blow and also for positive weighted $p$-harmonic functions $w$ in weighted manifolds under the Bakry-Émery curvature-dimension condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07470 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A quantitative second order estimate for (weighted) $p$-harmonic functions in manifolds under curvature-dimension condition Liu, Jiayin Zhang, Shijin Zhou, Yuan Analysis of PDEs Differential Geometry 58J60, 35J15, 35J62 We build up a quantitative second order Sobolev estimate of $ \ln w$ for positive $p$-harmonic functions $w$ in Riemannian manifolds under Ricci curvature bounded from blow and also for positive weighted $p$-harmonic functions $w$ in weighted manifolds under the Bakry-Émery curvature-dimension condition. |
| title | A quantitative second order estimate for (weighted) $p$-harmonic functions in manifolds under curvature-dimension condition |
| topic | Analysis of PDEs Differential Geometry 58J60, 35J15, 35J62 |
| url | https://arxiv.org/abs/2112.07470 |