The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910769450319872 |
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| author | Sepúlveda, Sebastián Flores Nornberg, Gabrielle |
| author_facet | Sepúlveda, Sebastián Flores Nornberg, Gabrielle |
| contents | We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$ at infinity. Our result is new even in the case of the fractional Laplacian, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_00969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay Sepúlveda, Sebastián Flores Nornberg, Gabrielle Analysis of PDEs 47G20, 45K05, 35B40, 35D40 We obtain a unique continuation result at infinity for fully nonlinear elliptic integro-differential operators of order 2s which satisfy the maximum and minimum principles in bounded subdomains, under the decay assumption $o(|x|^{-(N+2s)})$ at infinity. Our result is new even in the case of the fractional Laplacian, as it unveils the nonlocal nature of the decay in Landis conjecture, evolving from exponential to polynomial. |
| title | The Landis Conjecture For Nonlocal Elliptic Operators: Polynomial Decay |
| topic | Analysis of PDEs 47G20, 45K05, 35B40, 35D40 |
| url | https://arxiv.org/abs/2501.00969 |