Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912293474795520 |
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| author | Choulli, Mourad |
| author_facet | Choulli, Mourad |
| contents | Based on the three-ball inequality and the doubling inequality established in [23], we quantify the strong unique continuation established by Koch and Tataru [21] for elliptic operators with unbounded lower-order coefficients. We also derive a uniform quantitative strong unique continuation for eigenfunctions that we use to prove that two Dirichlet-Laplace-Beltrami operators are gauge equivalent whenever their corresponding metrics coincide in the vicinity of the boundary and their boundary spectral data coincide on a subset of positive measure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_09549 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem Choulli, Mourad Analysis of PDEs 35B60, 35J15, 35R30 Based on the three-ball inequality and the doubling inequality established in [23], we quantify the strong unique continuation established by Koch and Tataru [21] for elliptic operators with unbounded lower-order coefficients. We also derive a uniform quantitative strong unique continuation for eigenfunctions that we use to prove that two Dirichlet-Laplace-Beltrami operators are gauge equivalent whenever their corresponding metrics coincide in the vicinity of the boundary and their boundary spectral data coincide on a subset of positive measure. |
| title | Quantitative strong unique continuation for elliptic operators -- application to an inverse spectral problem |
| topic | Analysis of PDEs 35B60, 35J15, 35R30 |
| url | https://arxiv.org/abs/2209.09549 |