The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908420498522112 |
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| author | Dipierro, Serena Kwaśnicki, Mateusz Thompson, Jack Valdinoci, Enrico |
| author_facet | Dipierro, Serena Kwaśnicki, Mateusz Thompson, Jack Valdinoci, Enrico |
| contents | We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic operators.
The new approach to deal with these problems that we propose in this paper leverages Bochner's relation, allowing one to relate a one-dimensional Fourier transform of an odd function with a three-dimensional Fourier transform of a radial function.
In this way, Harnack inequalities for odd functions, which are essentially Harnack inequalities of boundary type, are reduced to interior Harnack inequalities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis Dipierro, Serena Kwaśnicki, Mateusz Thompson, Jack Valdinoci, Enrico Analysis of PDEs 35R11, 47G20, 35B50 We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic operators. The new approach to deal with these problems that we propose in this paper leverages Bochner's relation, allowing one to relate a one-dimensional Fourier transform of an odd function with a three-dimensional Fourier transform of a radial function. In this way, Harnack inequalities for odd functions, which are essentially Harnack inequalities of boundary type, are reduced to interior Harnack inequalities. |
| title | The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis |
| topic | Analysis of PDEs 35R11, 47G20, 35B50 |
| url | https://arxiv.org/abs/2411.11272 |