Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910346905649152 |
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| author | Lian, Yuanyuan |
| author_facet | Lian, Yuanyuan |
| contents | We investigate the interior pointwise $C^α$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability condition on the drift can be relaxed and the interior $C^α$ regularity for some $0<α<1$ has been obtained previously with the aid of Harnack inequality. In this paper, we prove the interior pointwise $C^α$ regularity for any $0<α<1$ provided that the drift is small. We obtain the regularity under three different types conditions on the drift. The proof is based on the energy inequality and the perturbation technique. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18161 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts Lian, Yuanyuan Analysis of PDEs We investigate the interior pointwise $C^α$ regularity for weak solutions of elliptic and parabolic equations with divergence-free drifts. For such equations, the integrability condition on the drift can be relaxed and the interior $C^α$ regularity for some $0<α<1$ has been obtained previously with the aid of Harnack inequality. In this paper, we prove the interior pointwise $C^α$ regularity for any $0<α<1$ provided that the drift is small. We obtain the regularity under three different types conditions on the drift. The proof is based on the energy inequality and the perturbation technique. |
| title | Interior pointwise $C^α$ regularity for elliptic and parabolic equations with divergence-free drifts |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.18161 |