On the blowup of quantitative unique continuation estimates for waves and applications to stability estimates
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916647757938688 |
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| author | Filippas, Spyridon Oksanen, Lauri |
| author_facet | Filippas, Spyridon Oksanen, Lauri |
| contents | In this paper we are interested in the blowup of a geometric constant $\mathfrak{C}(δ)$ appearing in the optimal quantitative unique continuation property for wave operators. In a particular geometric context we prove an upper bound for $\mathfrak{C}(δ)$ as $δ$ goes to $0$. Here $δ>0$ denotes the distance to the maximal unique continuation domain. As applications we obtain stability estimates for the unique continuation property up to the maximal domain. Using our abstract framework~\cite{FO25abstract} we also derive a stability estimate for a hyperbolic inverse problem. The proof is based on a global explicit Carleman estimate combined with the propagation techniques of Laurent-Léautaud. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the blowup of quantitative unique continuation estimates for waves and applications to stability estimates Filippas, Spyridon Oksanen, Lauri Analysis of PDEs 35B60, 35L05, 35Q93, 35R30 In this paper we are interested in the blowup of a geometric constant $\mathfrak{C}(δ)$ appearing in the optimal quantitative unique continuation property for wave operators. In a particular geometric context we prove an upper bound for $\mathfrak{C}(δ)$ as $δ$ goes to $0$. Here $δ>0$ denotes the distance to the maximal unique continuation domain. As applications we obtain stability estimates for the unique continuation property up to the maximal domain. Using our abstract framework~\cite{FO25abstract} we also derive a stability estimate for a hyperbolic inverse problem. The proof is based on a global explicit Carleman estimate combined with the propagation techniques of Laurent-Léautaud. |
| title | On the blowup of quantitative unique continuation estimates for waves and applications to stability estimates |
| topic | Analysis of PDEs 35B60, 35L05, 35Q93, 35R30 |
| url | https://arxiv.org/abs/2502.13040 |