On a fractional Alt-Caffarelli-Friedman-type monotonicity formula
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909834711924736 |
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| author | Ferrari, Fausto Giovagnoli, Davide Merlino, Enzo Maria |
| author_facet | Ferrari, Fausto Giovagnoli, Davide Merlino, Enzo Maria |
| contents | In this note, by exploiting mean value properties of $s$-harmonic functions, we introduce some monotonicity formulas in the nonlocal setting. We take into account intrinsically nonlocal functionals mimicking those introduced by Alt, Caffarelli and Friedman in the seminal work [Alt-Caffarelli-Friedman, Trans. Amer. Math. Soc. (1984)]. Our approach is purely nonlocal and does not rely on the extension technique. As a byproduct we also established interior nonlocal gradient estimates and a nonlocal analogue of the Bochner identity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a fractional Alt-Caffarelli-Friedman-type monotonicity formula Ferrari, Fausto Giovagnoli, Davide Merlino, Enzo Maria Analysis of PDEs 35R35, 35R11, 34K37 In this note, by exploiting mean value properties of $s$-harmonic functions, we introduce some monotonicity formulas in the nonlocal setting. We take into account intrinsically nonlocal functionals mimicking those introduced by Alt, Caffarelli and Friedman in the seminal work [Alt-Caffarelli-Friedman, Trans. Amer. Math. Soc. (1984)]. Our approach is purely nonlocal and does not rely on the extension technique. As a byproduct we also established interior nonlocal gradient estimates and a nonlocal analogue of the Bochner identity. |
| title | On a fractional Alt-Caffarelli-Friedman-type monotonicity formula |
| topic | Analysis of PDEs 35R35, 35R11, 34K37 |
| url | https://arxiv.org/abs/2509.25891 |