Propagation of smallness for solutions of elliptic equations in the plane
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917934654291968 |
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| author | Zhu, Yuzhe |
| author_facet | Zhu, Yuzhe |
| contents | We explore quantitative propagation of smallness for solutions of two-dimensional elliptic equations from sets of positive $δ$-dimensional Hausdorff content for any $δ>0$. In particular, the gradients of solutions to divergence form equations with Hölder continuous coefficients, as well as those of nondivergence form equations with measurable coefficients, can be quantitatively estimated from the small sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09800 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Propagation of smallness for solutions of elliptic equations in the plane Zhu, Yuzhe Analysis of PDEs We explore quantitative propagation of smallness for solutions of two-dimensional elliptic equations from sets of positive $δ$-dimensional Hausdorff content for any $δ>0$. In particular, the gradients of solutions to divergence form equations with Hölder continuous coefficients, as well as those of nondivergence form equations with measurable coefficients, can be quantitatively estimated from the small sets. |
| title | Propagation of smallness for solutions of elliptic equations in the plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.09800 |