Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909200485974016 |
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| author | Lian, Yuanyuan |
| author_facet | Lian, Yuanyuan |
| contents | In this paper, we obtain the interior pointwise $C^{k,α}$ ($k\geq 0$, $0<α<1$) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07214 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets Lian, Yuanyuan Analysis of PDEs In this paper, we obtain the interior pointwise $C^{k,α}$ ($k\geq 0$, $0<α<1$) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions. |
| title | Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.07214 |